Multiplying Out Two Brackets and Simplifying
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  • Introduction
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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
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Multiply out the two brackets and simplify:

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

x2 + 30x + 11

  • Question 2
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Multiply out the two brackets and simplify:

(x+8)(x+3) = 

 

8x2 + 24x + 29

x2 + 11x + 24

  • Question 3
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Multiply out the two brackets and simplify:

(x+5)(4x+2) = 

 

4x2 + 22x + 10

8x2 + 24x + 10

  • Question 4
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Multiply out the two brackets and simplify:

(3x+1)(2x+3) = 

 

 

6x2 + 11x + 3

8x2 + 29x + 10

  • Question 5
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Multiply out the two brackets and simplify:

(4x+2)(x-6) = 

 

4x2 + 26x + 12

4x2 - 22x - 12

  • Question 6
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Multiply out the two brackets and simplify:

(2x-6)(4x+6) = 

 

8x2 - 12x - 36

8x2 + 36x - 12

  • Question 7
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Multiply out the two brackets and simplify:

(4x-4)(3x-6) = 

 

12x2 - 36x - 24

12x2 - 36x + 24

  • Question 8
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Multiply out the two brackets and simplify:

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

 

4n2 + 16n - 20

4n2 + 17n - 20

  • Question 9
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Multiply out the two brackets and simplify:

(n+8)(n-8) =

 

n2 - 64

4n2 + 17n - 20

  • Question 10
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Multiply out and simplify:

(4n+1)2 =

 

16n2 + 1

16n2 + 8n + 1

Progress