Lesson 5, Topic 3
In Progress

# Factorising By Grouping

Lesson Progress
0% Complete

To factorise an expression containing four terms, you need to group the terms into pairs. Then factorise each pair of terms.

Example 1

a. $$\scriptsize x^2 + x \: – \: x \: – \:1 \\ \scriptsize = (x^2 + x) \: – \: x \: – \:1 \\ \scriptsize(x^2 + x) \: – \: (x + 1) \\ \scriptsize x(x+1) \: – \: 1 (x + 1) \\ \scriptsize = (x \: – \:1)( x + 1)$$

b. $$\scriptsize 6xy \: – \: 2x \: – \: 3y + 1 \\ \scriptsize (6xy \: – \: 2x) \: – \: (3y\: – \:1) \\ \scriptsize 2x(3y \: – \: 1) \: – \: 1(3y\: -\: 1) \\ \scriptsize (2x\: – \: 1)(3y\: – \:1)$$

c. $$\scriptsize 6x^2 \: + \: 15x \: – \: 2x \: – \: 5 \\ \scriptsize (6x^2 \: + \: 15x) \: – \: (2x \: +\: 5) \\ \scriptsize 3x(2x \: + \: 5) \: – \: 1(2x \: +\: 5) \\ \scriptsize (3x\: – \: 1)(2x \: +\: 5)$$

d. $$\scriptsize 4a^3y \: – \: 4a^2bx \: + \: 2ay^2 \: – \: 2bxy \\ \scriptsize (4a^3y \:- \: 4a^2bx) \:+ \: (2ay^2 \: -\: 2bxy) \\ \scriptsize 4a^2(ay \:- \: bx) \: + \: 2y(ay \: -\: bx) \\ \scriptsize (4a^2\: + \: 2y)(ay \: -\: bx)$$

e. $$\scriptsize 6x^2 \: + \: 2xy \: – \: 6xy \: – \: 2y^2 \\ \scriptsize (6x^2 \: + \: 2xy) \: – \: (6xy \: +\: 2y^2) \\ \scriptsize 2x(3x \: + \: y) \: – \: 2y(3x \: + \: y) \\ \scriptsize (2x\: – \: 2y)(3x \: + \: y)$$

error: