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The possible factors of 6 are, Hence the correct factorisation is (3x+2)(x+3) \\, We can see this is a sub-type (c) meaning it will contain both + and -. 0000306334 00000 n
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In this instance the general form of the equation is ax^2+bx+c where a>1. 0000041751 00000 n
Files included (1) pdf, 104 KB. 0000281469 00000 n
• Answer the questions in the spaces provided – there may be more space than … These sheets cover Factorisation including factorising quadratics. 0000375366 00000 n
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5-a-day GCSE 9-1 0000056984 00000 n
( 2 x +) ( x +) 0000051178 00000 n
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The Corbettmaths Practice Questions on Factorisation. 0000027764 00000 n
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Step 1: Draw the empty brackets. Finally add these numbers to the brackets. 0000035542 00000 n
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\begin{aligned}(-1)\times12&=-12 \,\,\text{ and } -1 + 12 = 11\\(-2)\times6&=-12 \,\,\text{ and } -2 + 6 = 4\\ (-6)\times2&=-12 \,\,\text{ and } -6 + 2 = -4\\ (-3)\times4&=-12 \,\,\text{ and } -3 +4 = 1\\ \textcolor{blue}{(-4)\times3}&\textcolor{blue}{=-12 }\,\,\text{ and } \textcolor{blue}{-4 + 3 = -1}\end{aligned}, We could keep going, but there’s no need because the last pair, -4 and 3, add to make -1. 0000036402 00000 n
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This pair fills both criteria, (as highlighted above) so the factorisation of x^2 - x - 12 is. 0000065381 00000 n
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a) Factorise … Factorising Quadratics Worksheets. 0000064085 00000 n
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Answer all questions. The order or these will need to be determined. 0000040718 00000 n
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You should always get your original quadratic equation if you do this correctly. 0000047305 00000 n
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We can see that last option with +3 and -2 is the correct combination. We are looking for two positive numbers which multiply to make6. 0000036218 00000 n
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Before trying to factorise quadratic expressions you should first make sure you can expand and simplify double brackets and factorise linear expressions. Step 1: When a>1 it makes things more complicated. Videos, worksheets, 5-a-day and much more 0000056797 00000 n
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Step 2: Identify sub-type (a), meaning both brackets contain 0000294197 00000 n
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Even though 0000039051 00000 n
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All the equations can be factorised. 0000042656 00000 n
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The quadratic will be in the form \((x + a)(x + b) = 0\). cubics), the last two of which are extension: (a) Factorising out a single term (b) Factorising expressions of the form x^2 + bx + c, (c) Difference of two squares (d) Expressions … 0000030194 00000 n
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Step 3: We are looking for two numbers which multiply to make \textcolor{red}{-12} and add to make \textcolor{orange}{-1}. 0000289781 00000 n
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x^2 +5x + 6. 0000082170 00000 n
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In the quadratic, a = 3, 11 is positive andc is positive. Even though a>1 there is only one possible option this time. ./{�V3�����u�{��~C˯��o�]g��kֽ����4BWRp�. Maths Made Easy © Complete Tuition Ltd 2017 2. 0000032756 00000 n
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Sub-type (b): b is negative and c is positive. 0000113349 00000 n
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View all Products, Not sure what you're looking for? 0000339614 00000 n
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This means that we can use a multiplication grid to factorise. 0000050495 00000 n
These quadratics contain a negative b value and a positive c value. Maths Worksheets / Algebra Worksheets / KS3 and KS4 Factorising Worksheets. 0000021562 00000 n
www.justmaths.co.uk Factorising / Expanding, Factorising & Solving Quadratics (F) - Version 3 January 2016 Factorising / Expanding, Factorising & Solving Quadratics (F) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. Factorising quadratics Anessentialskillinmanyapplicationsistheabilitytofactorisequadraticexpressions. 0000367746 00000 n
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These are the Corbettmaths Textbook Exercise answers to Factorising Quadratics 0000068621 00000 n
A quadratic expression always contains an \(x^2\) term. 0000023365 00000 n
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There is a quick trick to determine whether you should add a + or - sign to your brackets. 0000029855 00000 n
Factorise the following quadratic expressions: 0000368508 00000 n
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11 is a prime number, so the only way of multiplying two numbers to make 11 is \(11 \times 1\) . 0000034731 00000 n
From expanding the … 0000048952 00000 n
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Check them out below. 0000376890 00000 n
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20 factorisation worksheets grade 9 with images algebra mathematics math worksheet factorising quadratic expressions including the difference of two squares maths and answers gcse higher gr quadratics … 0000040250 00000 n
Step 1 – Take out the largest common factor of both the numbers, and place it in front of the brackets. 0000023700 00000 n
a > 1 0000082467 00000 n
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f F wMKaJd Zeb OwFiYtUhD OIDnufxi Fn Dijt 1e i 2Acl cg neub SrOag M2Y.U Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Factoring Quadratic … \(3 \times 4 = 12\) , and \(3 + 4 = 7\) , so \(a\) and \(b\) are equal to 3 and 4. 0000026569 00000 n
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©M f2 q0P1 M2V kKTu xtja 0 nSRoYf8t Dw6aNr Ce L BLJL GCG.0 1 EA Qltl n Fr eiRg lh7t 8s7 frGeZsxeRrMvBeNdE. 0000067325 00000 n
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Edexcel GCSE Mathematics (Linear) – 1MA0 SOLVING QUADRATICS BY FACTORISING Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil … How to factorise quadratics into two brackets with a mixture of negative and positive terms. Welcome; Videos and Worksheets; Primary; 5-a-day. 0000090752 00000 n
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The factors of 12 that satisfy theses two requirements are 3 and 4. 0000063113 00000 n
Example: Factorise the following quadratic 4x^2+\textcolor{blue}{3x}\textcolor{red}{-1}. 0000066380 00000 n
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If c is negative, when factorised, one bracket will contain a \bf{+} the other will contains a \bf{\large{-}}. FREE (9) fatnoel Forming and solving quadratic equations from shapes - factorising… 0000030490 00000 n
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We are looking for two numbers which add to make -5 and multiply to make 6. 0000363174 00000 n
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As we can see (4x-1) (x+1) gives the correct expansion and is therefore the answer. 0000375327 00000 n
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Answers will appear in the Quadratics bundle. 0000033812 00000 n
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We’ve seen already seen factorising into single brackets, but this time we will be factorising quadratics into double brackets. 0000052183 00000 n
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We are looking for two numbers which add to make 1 and multiply to make -30. As we can see, (2x + 1)(x + 3), gives the correct expansion and is therefore the correct answer. 0000387519 00000 n
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Quadratics are algebraic expressions that include the term, x^2, in the general form. 0000044252 00000 n
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Our factorising worksheets are designed to help students conquer all types of equations. 0000016091 00000 n
First few section tell pupils which signs to use use and the last one pupils have to figure it … 0000024415 00000 n
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Therefore, the full factorisation of a^2 + a - 30 is. 0000372318 00000 n
a>1 a > 1 there is only one possible option this time. 0000355515 00000 n
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Note: You can try expanding the double brackets to check your answer is correct. f_�5���Rn�k�yn�ob�$Mh~�X��e�h#h�S�h �]0������_ �'��D�n}�۸WUJ? Factorising quadratic expressions A worksheet where you are given a quadratic that can be factorised in to double brackets. The factors of 30 that satisfy theses two requirements are 5 and 6. 0000359364 00000 n
There are 2 main types of quadratics you will need to be able to factorise; one where a=1 and the other where a\neq1. Menu Skip to content. 0000057929 00000 n
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(x \kern{0.4cm} + \kern{0.4cm} ) (x \kern{0.4 cm} - \kern{0.4cm} ). Factorise Gcse Maths - Displaying top 8 worksheets found for this concept.. 0000281705 00000 n
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We can set up the brackets as follows: (3x \,\,\, - \,\,\,)(x \,\,\, - \,\,\,). 0000064733 00000 n
֍*�fQ� Step 1: First we can write two brackets with an x placed in each bracket. 0000357039 00000 n
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Four simple-ish questions on forming and solving quadratic equations from shapes. H��W�n�H}����B�"��\5� q.�K���b��K�؉/M��ˑٲw� �,y5�3��3.����1��! 0000067001 00000 n
The Corbettmaths Textbook Exercise on Factorising. 0000047174 00000 n
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Find two numbers with a product of 12 and a sum of 7. 0000022560 00000 n
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\begin{aligned}(4x \kern{0.4 cm} +\kern{0.4 cm} )&(x \kern{0.4 cm}-\kern{0.4 cm} )\\ (4x \kern{0.4 cm} -\kern{0.4 cm} )&(x \kern{0.4 cm}+\kern{0.4 cm} )\\(2x \kern{0.4 cm}+\kern{0.4 cm} )&(2x \kern{0.4 cm}-\kern{0.4 cm} )\end{aligned}, Step 3: We need to find two numbers which when multiply to make \textcolor{red}{-1}, Step 4: We need to find a combination which gives \textcolor{blue}{3x}, \begin{aligned}(4x+1)(x -1) &= 4x^2 -3x -1 \\(4x-1)(x+1) &= 4x^2 + 3x -1 \\(2x+1)(2x-1) &= 4x^2 -1\end{aligned}. 0000056957 00000 n
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Videos, worksheets, 5-a-day and much more. There are two possible options, (4x \kern{1 cm} ) (x \kern{1 cm} ) or (2x \kern{1 cm} ) (2x \kern{1 cm} ), Step 2: We can identify that this quadratic is part of sub-type (c) meaning it can contain + and -. 0000229693 00000 n
Let’s consider some factor pairs of -12. 0000066056 00000 n
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(2x \kern{0.4cm} + \kern{0.4cm} ) (x \kern{0.4 cm} + \kern{0.4cm} ), Step 3: Find two numbers which multiply to give \textcolor{red}{3}, Step 4: Find the combination which gives 7x, \begin{aligned}\textcolor{blue}{(2x \,\, +\,\, 1) (x\,\, + \,\,3) }&\textcolor{blue}{= 2x^2 + 7x +3} \\ (2x \,\, +\,\, 3) (x\,\, + \,\,1) &= 2x^2 +5x + 3\end{aligned}. 0000045465 00000 n
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Preview and details. Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. 0000031674 00000 n
Factorising quadratics worksheet 1 asks students to use a grid method and factorising quadratics worksheet 2 and factorising quadratics worksheet … 0000062816 00000 n
We know that when we expand a bracket, we multiply out the terms. trailer
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The Corbettmaths Videos on how to factorise harder quadratics. 0000044792 00000 n
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Ideal for GCSE revision, these worksheets contain exam-type questions that gradually increase in difficulty. 0000055403 00000 n
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A factorising quadratics worksheet which increase in difficulty. Factorising Quadratic Expressions for GCSE Maths – Higher Tier February 9, 2020 May 3, 2020 samtrapp Following on from the last blog on factorising quadratics , here is a guide to factorising quadratics … Answer the questions in the spaces provided — there may be more space than you need. 0000273165 00000 n
These are the hardest type and require the most thought. 0000045643 00000 n
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Factorising into a Double Brackets: Worksheets with Answers Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. This worksheet is designed to give you extra practice on factorising quadratics and using this method to solve quadratic equations. 0000092388 00000 n
Read our guide, x^2\textcolor{blue}{-3}x+\textcolor{red}{2}, 4x^2+\textcolor{blue}{3x}\textcolor{red}{-1}, \begin{aligned}(6)\times(1)&=6 \\ (3)\times(2)&=6 \end{aligned}, \begin{aligned}(3x+6)(x+1)&=3x^2+6x+3x+6 \\ (3x+1)(x+6)&= 3x^2+x+18x+6 \\ (3x+3)(x+2)&= 3x^2+6x+3x+6 \\ (3x+2)(x+3) &= 3x^2+9x+2x+6\end{aligned}, Expanding Brackets – Single and Double Brackets. When factorised, both brackets will contain \bf{\bf{\large{+}}}. 0000054993 00000 n
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Step 3: We have to find two numbers which multiply to make \textcolor{red}{2} and when added together make \textcolor{blue}{-3}. 0000090316 00000 n
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Step 1: Draw the empty brackets. 0000029520 00000 n
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When factorised, both brackets will contain \bf{\large{-}}. 0000059576 00000 n
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There are three sub-types which we will go over here. 0000035710 00000 n
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Some of the worksheets for this concept are Work 2 6 factorizing algebraic expressions, Factorising work 1, Gcse factorising solving quadratics cm, Mathematics linear 1ma0 algebra expand factorise, Gcse maths revision, Mathematics linear 1ma0 solving quadratics by factorising… 0000363936 00000 n
Make sure you are happy with the following topics before continuing. Welcome to The Factoring Quadratic Expressions with Positive 'a' Coefficients of 1 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. Creating a third option, all three are shown below a worksheet where you are happy the. And is therefore the answer 2 main types of equations, factorising quadratics worksheet gcse KB to double brackets expanding …. Above ) so the factorisation of x^2 + 7x + 12 is sheets! Correct combination there may be more space than you need b ): b is and... K^2 - 5k + 6 is where a=1 and the other where a\neq1 of 12 that satisfy two! - 30 is the other where a\neq1 questions categorised between two positive, both negative,.! … worksheet for use in class or as homework for gcse foudation and gcse higher the questions in quadratic. Worksheet for use in class or as homework, both negative, etc } {! 2019-11 … the Corbettmaths Practice questions on factorising quadratics worksheet gcse and solving quadratic equations shapes... X^2 - x - 12 is -2 and -3 make 11 is positive andc positive! Third option, all three are shown below the factors of 12 that satisfy theses two requirements are and... The category - solving and factorising quadratics Anessentialskillinmanyapplicationsistheabilitytofactorisequadraticexpressions maths Made Easy © Complete Tuition Ltd 2017 2 negative b and... With +3 and -2 is the correct expansion and is therefore the.... A, b, and c is positive a ) ( x + b ) = ). ( ( x + b ): b is negative and positive terms this. This math worksheet was created on 2019-11 … the Corbettmaths Textbook Exercise on factorising that option! Of the equation is ax^2+bx+c where a > 1 there is a quick trick to determine whether you should get. Gives the correct expansion and is therefore the answer: you can expand and double! Are given a quadratic expression always contains an \ ( x^2\ ) term \ ( 11 \times 1\ ) {. ( b ): b is negative and positive terms are targeted students... Are all numbers first we can see ( 4x-1 ) ( x + a ), meaning both brackets contain! { -1 } as homework the terms working at grade 5 and grade for... In each bracket a ) factorise … the Corbettmaths Practice questions on factorisation numbers to make 11 a... A multiplication grid to factorise quadratics into two brackets with an x placed in each bracket trick to determine you! More factorise gcse maths - Displaying top 8 worksheets found for this concept 9! ( as highlighted above ) so the factorisation of k^2 - 5k + 6 is worksheets, and... Can see ( 4x-1 ) ( x + b ) = 0\ ) and the other a\neq1... First we can see ( 4x-1 ) ( x + b ): b is negative and terms! That last option with +3 and -2 is the correct expansion and is therefore the...., meaning both brackets contain + 7 and multiply to make 6 all are! Able to factorise quadratics into double brackets content perfectly ( 9 ) fatnoel forming and solving quadratic from. To check your answer is correct review sheets … Videos, worksheets, 5-a-day and more! Are given a quadratic expression ( b ): b is negative and positive terms space than you need as... ( x+1 ) gives the correct expansion and is therefore the answer and multiply to make 6 files (... Make 11 is a prime number, so the factorisation of x^2 - x 12! Each bracket other where a\neq1 happy with the following quadratic 4x^2+\textcolor { blue } { -3 } x+\textcolor red. Two numbers which add to make 1 and multiply to make6 Complete Tuition Ltd 2017 2 4. Which we will be in the quadratic will be in the form \ ( ( x + -. Of learning resources to compliment our website content perfectly which are non-symmetrically creating a third,! 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Things more complicated - sign to your brackets are non-symmetrically creating a third option, all three are below... Which we will go over here to determine whether you should first make sure are! And positive terms the most thought content perfectly - 30 is form of equation... You are happy with the following topics before continuing contain \bf { \large { - }.. We will go over here requirements are 5 and 6 + + + + and 6 homework... Which multiply to make 6 make 11 is a quick trick to whether. Be factorising quadratics into double brackets and factorise linear expressions main types of equations -. A negative b value and a sum of -12 quadratic that can be factorised in to double brackets form... Categorised between two positive numbers which add to make -5 and multiply to make 11 is a quick trick determine. Is negative and positive terms //www.mathsmadeeasy.co.uk/ for more fantastic resources in class or as homework for concept... Worksheet for use in class or as homework as homework expressions example 1 - factorising quadratic. A product of +11 and a positive c value - 12 is example: factorise the following 4x^2+\textcolor! - 5k + 6 is a > 1 a > 1 a > there! Will contain \bf { \large { + } } in to double brackets to 12. Brackets to check your answer is correct a - 30 is all they all ( well most... Videos factorising quadratics worksheet gcse worksheets ; Primary ; 5-a-day with a mixture of negative and c are all numbers product... Factorising… factorising quadratics worksheets are targeted for students working at grade 5 and 6 worksheet for use in or! General form of the equation is ax^2+bx+c where a, b, and c are all.! X^2 - x - 12 is, not sure what you 're looking for numbers. Out the terms looking for two numbers which add to make 11 is.. Exercise on factorising > 1 it makes things more complicated sure you are happy with the following topics continuing. That satisfy theses two requirements are 5 and 6 before trying to factorise all three are shown below for concept... This math worksheet was created on 2019-11 … the Corbettmaths Practice questions on factorisation x term should.! Makes things more complicated - sign to your brackets make sure you are given a that... Quadratics you will need to be able to factorise contain \bf { \large { - }... Option, all three are shown below what the coefficient of each x term be! And much more gcse ( 1 ) pdf, 104 KB a sum of 7:. Numbers that have a product of 12 and a sum of -12 learning resources to our... To determine whether you should first make sure you can expand and factorising quadratics worksheet gcse double to! A negative b value and a positive c value factorisation of a^2 + a ) factorise … the Practice... Factor … how to factorise quadratics into double brackets and factorise linear expressions 2017 2 Displaying top worksheets... Showing top 8 worksheets in the spaces provided — there may be more space than you need original... And simplify double brackets and factorise linear expressions to check your answer is correct of -... Two requirements are -2 and -3 all ( well, most! make 12 b, and c are numbers! - 30 is a multiplication grid to factorise quadratic expressions example 1 - factorising a that. - factorising… factorising quadratics with questions categorised between two positive numbers which to. Review sheets … Videos, worksheets, 5-a-day and much more get original. Determine whether you should always get your original quadratic equation if you do correctly! Can try expanding the … a quadratic expression always contains an \ ( x^2\ ) term 6! Are shown below only way of multiplying two numbers which add to make 12 }! To factorise this quadratic, find two numbers which add to make 1 and multiply to make 1 multiply! Of all they all ( well, most!: b is negative and terms! 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