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Expand Products of Two Binomials

In this worksheet, students will use the FOIL method to expand double brackets.

'Expand Products of Two Binomials' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation, Algebraic Expressions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

There are many methods for expanding double brackets.

One of them is called FOIL. Each letter stands for the terms we will be multiplying out.

 

F - First

O - Outer

I - Inner

L - Last

 

Remember to include the signs in front of each term when multiplying them out.

 

After we have multiplied each of those, we are going to simplify the expression by collecting like terms.

 

Here's an example. Expand and simplify (x + 5)(x + 6).

 

F: x × x = x² 

O: x × +6 = +6x

I: +5 × x = +5x

L: +5 × +6 = +30

 

Now let's simplify by collecting like terms (highlighted): 

x² + 6x + 5x + 30 = x² + 11x + 30

Expand and simplify

(x + 2)(x + 3)

x² + 6

x² + 11x

x² + 5x + 6

12x²

Eric tried using the foil method to expand (2y + 4)(3y - 5)

Here are his working.

F: 2y × 3y = 5y

O: 2y × -5 = -10y

I: 4 × 3y = 12y

L: 4 × -5 = -1

How many mistakes did he make?

0 mistakes

1 mistake

2 mistakes

3 mistakes

Expand and simplify

(x + 8)(x + 5)

14x² + 40

x² + 40x + 13

x² + 13x +13

x² + 13x + 40

Match each set of double brackets with their expanded form.

Column A

Column B

(x - 2)(x + 7)
x² - 5x - 14
(x + 2)(x + 7)
x² + 5x - 14
(x + 2)(x - 7)
x² + 9x + 14
(x - 2)(x - 7)
x² - 9x + 14

Expand (x - 2)².

x² - 4

x² + 4

x² - 4x + 4

x² + 4x + 4

Find an expression for the area of this rectangle:

(a + 7)(2a + 3)

3a + 10

2a² + 17a + 21

2a² + 21

Spot a mistake! Underline which part of the answer is incorrect.

Expand (x + 7)(x + 7).

Workings out & solution: x² + 7x + 7x + 14 = x² + 14x + 14.

x² + 14x + 14

What is the area of this triangle?

(3x + 4)(2x - 4)

0.5(3x + 4)(2x - 4)

6x² - 4x - 16

3x² - 2x - 8

Match the brackets to their expanded versions. Use the FOIL method to help you.

Column A

Column B

(x - 6)²
x² - 36
(x - 6)(x + 6)
x² + 7x + 6
(x + 6)²
x² - 12x + 36
(x + 6)(x + 1)
x² + 12x + 36

Spot the mistake! Underline the part of the answer which is incorrect.

Expand (3x + 6)(2x - 5).

Workings and answer: 5x² - 15x + 12x - 30 =  5x² - 3x - 30

5x² - 3x - 30
  • Question 1

Expand and simplify

(x + 2)(x + 3)

CORRECT ANSWER
x² + 5x + 6
EDDIE SAYS
Did you use the FOIL method? F: x × x = x² O: x × 3 = 3x I: 2 × x = 2x L: 2 × 3 = 6 Now put these all together and simplify. x² + 3x + 2x + 6 = x² + 5x + 6
  • Question 2

Eric tried using the foil method to expand (2y + 4)(3y - 5)

Here are his working.

F: 2y × 3y = 5y

O: 2y × -5 = -10y

I: 4 × 3y = 12y

L: 4 × -5 = -1

How many mistakes did he make?

CORRECT ANSWER
2 mistakes
EDDIE SAYS
Eric made two mistakes. The first one was when he was multiplying out first terms of the brackets. The correct working should read: F: 2y × 3y = 6y² The second mistake is in the last line of his working. He did not multiply the terms, but added them. The correct working should be: L: 4 × -5 = -20
  • Question 3

Expand and simplify

(x + 8)(x + 5)

CORRECT ANSWER
x² + 13x + 40
EDDIE SAYS
The last option is correct as it shows that a correct method for expanding and simplifying was used. Let's have a look. F: x × x = x² O: x × +5 = +5x I: +8 × x = +8x L: +8 × +5 = +40 Now we need to simplify x² + 5x + 8x + 40. This gives us an answer of x² + 13x + 40.
  • Question 4

Match each set of double brackets with their expanded form.

CORRECT ANSWER

Column A

Column B

(x - 2)(x + 7)
x² + 5x - 14
(x + 2)(x + 7)
x² + 9x + 14
(x + 2)(x - 7)
x² - 5x - 14
(x - 2)(x - 7)
x² - 9x + 14
EDDIE SAYS
Did you use FOIL?
  • Question 5

Expand (x - 2)².

CORRECT ANSWER
x² - 4x + 4
EDDIE SAYS
Did you spot that this is really double brackets? Squaring means multiplying by itself, so (x - 2)² is really (x - 2)(x - 2). Using FOIL to expand these brackets we get: x² - 2x - 2x + 4 = x² - 4x + 4
  • Question 6

Find an expression for the area of this rectangle:

CORRECT ANSWER
(a + 7)(2a + 3)
2a² + 17a + 21
EDDIE SAYS
How do you find the area of a rectangle? Multiply length and width. So one of the correct options is (a + 7)(2a + 3). But we can also expand the brackets using the FOIL method and this will give us 2a² + 17a + 21, so this is also a correct answer.
  • Question 7

Spot a mistake! Underline which part of the answer is incorrect.

Expand (x + 7)(x + 7).

Workings out & solution: x² + 7x + 7x + 14 = x² + 14x + 14.

CORRECT ANSWER
+ 14x + 14
EDDIE SAYS
+ 14 is incorrect, it should be 49! (7 × 7 - Last in the FOIL method).
  • Question 8

What is the area of this triangle?

CORRECT ANSWER
0.5(3x + 4)(2x - 4)
3x² - 2x - 8
EDDIE SAYS
Another tricky one! Did you remember that to find the area of a triangle you need to multiply base and height and then divide by 2? The correct answers are: 0.5(3x + 4)(2x - 4) AND 3x² - 2x - 8 (if you expand it using FOIL).
  • Question 9

Match the brackets to their expanded versions. Use the FOIL method to help you.

CORRECT ANSWER

Column A

Column B

(x - 6)²
x² - 12x + 36
(x - 6)(x + 6)
x² - 36
(x + 6)²
x² + 12x + 36
(x + 6)(x + 1)
x² + 7x + 6
EDDIE SAYS
I hope you remember that (x - 6)² means (x - 6)(x - 6) and that (x + 6)² is (x + 6)(x + 6). Use FOIL to expand the brackets. (x - 6)² = (x - 6)(x - 6) = x² - 6x - 6x + 36 = x² - 12x + 36 (x + 6)² = (x + 6)(x + 6) = x² + 6x 6x + 36 = x² + 12x + 36
  • Question 10

Spot the mistake! Underline the part of the answer which is incorrect.

Expand (3x + 6)(2x - 5).

Workings and answer: 5x² - 15x + 12x - 30 =  5x² - 3x - 30

CORRECT ANSWER
5x² - 3x - 30
EDDIE SAYS
Here the first step of FOIL is incorrect: 3x × 2x is 6x²! The correct answer should read 6x² - 3x - 30
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