Multiplying Out Two Brackets and Simplifying
• Introduction

In this worksheet, you must multiply out two algebraic brackets.

Method

When we multiply out brackets we split the first bracket and multiply each term by the second bracket, as follows:

(a + b)(BANANA) = a(BANANA) + b(BANANA)

(a - b)(BANANA) = a(BANANA) - b(BANANA)

Examples

(x + 3)(x - 6) = x(x - 6) + 3(x - 6) = x- 6x + 3x - 18
= x- 3x - 18

(2x - 1)2 = (2x - 1)(2x - 1) = 2x(2x - 1) - 1(2x - 1) = 4x- 2x - 2x + 1
= 4x- 4x + 1

• Question 1

Multiply out the two brackets and simplify:

 (x+5)(x+6) =
x2 + 11x + 30

x2 + 30x + 11

• Question 2

Multiply out the two brackets and simplify:

 (x+8)(x+3) =

8x2 + 24x + 29

x2 + 11x + 24

• Question 3

Multiply out the two brackets and simplify:

 (x+5)(4x+2) =

4x2 + 22x + 10

8x2 + 24x + 10

• Question 4

Multiply out the two brackets and simplify:

 (3x+1)(2x+3) =

6x2 + 11x + 3

8x2 + 29x + 10

• Question 5

Multiply out the two brackets and simplify:

 (4x+2)(x-6) =

4x2 + 26x + 12

4x2 - 22x - 12

• Question 6

Multiply out the two brackets and simplify:

 (2x-6)(4x+6) =

8x2 - 12x - 36

8x2 + 36x - 12

• Question 7

Multiply out the two brackets and simplify:

 (4x-4)(3x-6) =

12x2 - 36x - 24

12x2 - 36x + 24

• Question 8

Multiply out the two brackets and simplify:

 (n+5)(4n-4) =

4n2 + 16n - 20

4n2 + 17n - 20

• Question 9

Multiply out the two brackets and simplify:

 (n+8)(n-8) =

n2 - 64

4n2 + 17n - 20

• Question 10