# Multiplying Out Two Brackets and Simplifying

In this worksheet, students multiply out two binomials.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:

### QUESTION 1 of 10

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)(c) = a(c) + b(c)

(a - b)(c) = a(c) - b(c)

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

Multiply out the two brackets and simplify:

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

x2 + 30x + 11

Multiply out the two brackets and simplify:

 (x+8)(x+3) =

8x2 + 24x + 29

x2 + 11x + 24

Multiply out the two brackets and simplify:

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

4x2 + 22x + 10

8x2 + 24x + 10

Multiply out the two brackets and simplify:

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

6x2 + 11x + 3

8x2 + 29x + 10

Multiply out the two brackets and simplify:

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

4x2 + 26x + 12

4x2 - 22x - 12

Multiply out the two brackets and simplify:

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

8x2 - 12x - 36

8x2 + 36x - 12

Multiply out the two brackets and simplify:

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

12x2 - 36x - 24

12x2 - 36x + 24

Multiply out the two brackets and simplify:

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

4n2 + 16n - 20

4n2 + 17n - 20

Multiply out the two brackets and simplify:

 (n+8)(n-8) =

n2 - 64

4n2 + 17n - 20

Multiply out and simplify:

 (4n+1)2 =

16n2 + 1

16n2 + 8n + 1

• Question 1

Multiply out the two brackets and simplify:

 (x+5)(x+6) =
x2 + 11x + 30
• Question 2

Multiply out the two brackets and simplify:

 (x+8)(x+3) =

x2 + 11x + 24
• Question 3

Multiply out the two brackets and simplify:

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

4x2 + 22x + 10
• Question 4

Multiply out the two brackets and simplify:

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

6x2 + 11x + 3
• Question 5

Multiply out the two brackets and simplify:

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

4x2 - 22x - 12
• Question 6

Multiply out the two brackets and simplify:

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

8x2 - 12x - 36
• Question 7

Multiply out the two brackets and simplify:

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

12x2 - 36x + 24
• Question 8

Multiply out the two brackets and simplify:

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

4n2 + 16n - 20
• Question 9

Multiply out the two brackets and simplify:

 (n+8)(n-8) =

n2 - 64
• Question 10

Multiply out and simplify:

 (4n+1)2 =

16n2 + 8n + 1
---- OR ----

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