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Expand Products of Two Binomials

In this worksheet, students will use the grid method to expand products of two binomials.

'Expand Products of Two Binomials' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Expanding double brackets could be done using a variety of methods, but today we will focus on the grid method. Have a look at an example.

Expand (x + 3)(x + 2).

First, we will set up a table like the one below:

See how the first bracket is on the top and the second bracket on the side.

Now we are going to multiply out each element.

You need to make sure that the signs are correct. Positive multiplied by a positive is a positive. Negative multiplied by a negative is also a positive. But a negative multiplied by a positive is a negative!

Now take all the terms we've just placed in a table and simplify as much as possible.

x² + 3x + 2x + 6 = x² + 5x + 6

(x + 3)(x + 2) = x² + 5x + 6

Here is a table for expanding (x + 5)(x + 3).

What is the simplified answer?

26x³

x² + 3x +5x + 15

x² + 8x + 15

x² + 15x + 15

What is the missing element in this grid?

- 11

+ 11

- 30

+ 30

What is the missing number in this grid?

+ 12

+ 3

- 3

- 12

Use the grid method to expand and simplify (x + 2)(x - 5).

x² + 3x - 10

x² - 3x + 10

x² + 3x + 10

x² - 3x - 10

Match the brackets with correct simplified expansions.

Use a grid like the one below to help you.

Column A

Column B

(2x + 5)(x + 3)
2x² - x - 15
(2x - 5)(x + 3)
2x² - 11x + 15
(2x - 5)(x - 3)
2x² + x - 15
(2x + 5)(x - 3)
2x² + 11x + 15

Pick the other bracket that will multiply out with (2x + 1) to give 2x² + 3x + 1.

The grid below might help you to make a decision.

 (2x - 1)(x + 1)(x + 3)(x - 3)
(2x + 1)

Find the area of the rectangle below.

3x² + 5x - 12

3x² - 5x - 12

3x² + 5x + 12

3x² - 5x + 12

Match the bracket with correct expansions.

You might want to use the grid below to help you.

Column A

Column B

(5x - 6)(2x + 3)
10x² - 27x + 18
(5x + 6)(2x + 3)
10x² + 3x - 18
(5x - 6)(2x - 3)
10x² - 3x - 18
(5x + 6)(2x - 3)
10x² + 27x + 18

Expand and simplify (5x + 4)².

25x² + 16

25x² + 4

25x² + 8x + 16

25x² + 40x + 16

Spot the mistake!

Expand (4x + 1)(x - 5).

Workings out:

4x² + 20x + x - 5 = 4x² + 21x - 5

4x² + 20x + x - 5
  • Question 1

Here is a table for expanding (x + 5)(x + 3).

What is the simplified answer?

CORRECT ANSWER
x² + 8x + 15
EDDIE SAYS
Once you have the table filled out, you need to simplify the terms. 3x and 5x can be added giving 8x. Nothing else can be simplified, so the final answer is x² + 8x + 15.
  • Question 2

What is the missing element in this grid?

CORRECT ANSWER
+ 30
EDDIE SAYS
Remember we multiply out each of the terms to fill out the grid! - 6 × - 5 = + 30, so this is the missing value.
  • Question 3

What is the missing number in this grid?

CORRECT ANSWER
+ 3
EDDIE SAYS
The answer is + 3 because to get + 3x in the second row, you need to multiply x by + 3. Similarly, to get - 18 in the third row, you need to multiply - 6 by + 3.
  • Question 4

Use the grid method to expand and simplify (x + 2)(x - 5).

CORRECT ANSWER
x² - 3x - 10
EDDIE SAYS
Expanding (x + 2)(x - 5) should give you x² + 2x - 5x - 10. Remember to simplify the terms: you can simplify +2x - 5x = -3x So the final answer is x² - 3x - 10.
  • Question 5

Match the brackets with correct simplified expansions.

Use a grid like the one below to help you.

CORRECT ANSWER

Column A

Column B

(2x + 5)(x + 3)
2x² + 11x + 15
(2x - 5)(x + 3)
2x² + x - 15
(2x - 5)(x - 3)
2x² - 11x + 15
(2x + 5)(x - 3)
2x² - x - 15
EDDIE SAYS
Did you use the grid? Put the terms of the first brackets at the top and the terms of the second bracket down the side. The difficulty here is the different signs. Be very careful how you multiply out the terms. Remember: positive × positive = positive positive × negative = negative negative × positive = negative negative × negative = positive
  • Question 6

Pick the other bracket that will multiply out with (2x + 1) to give 2x² + 3x + 1.

The grid below might help you to make a decision.

CORRECT ANSWER
 (2x - 1)(x + 1)(x + 3)(x - 3)
(2x + 1)
EDDIE SAYS
The correct answer is (2x + 1)(x + 1) as these two brackets will multiply out to give 2x² +x + 2x + 1 = 2x² + 3x + 1
  • Question 7

Find the area of the rectangle below.

CORRECT ANSWER
3x² + 5x - 12
EDDIE SAYS
The area of this rectangle can be expressed as (3x - 4)(x + 3) (length × width). Using a grid method to expand the brackets we get the final answer of 3x² + 5x - 12.
  • Question 8

Match the bracket with correct expansions.

You might want to use the grid below to help you.

CORRECT ANSWER

Column A

Column B

(5x - 6)(2x + 3)
10x² + 3x - 18
(5x + 6)(2x + 3)
10x² + 27x + 18
(5x - 6)(2x - 3)
10x² - 27x + 18
(5x + 6)(2x - 3)
10x² - 3x - 18
EDDIE SAYS
These look all very similar, don't they? Make sure you get the signs right here, they make all the difference! When you place numbers in the grid, always place them together with a sign immediately before them.
  • Question 9

Expand and simplify (5x + 4)².

CORRECT ANSWER
25x² + 40x + 16
EDDIE SAYS
Did you spot that this question is actually about expanding double brackets? Squaring means multiplying by itself, so (5x + 4)² means (5x + 4)(5x + 4). The correct answer is 25x² + 40x + 16.
  • Question 10

Spot the mistake!

Expand (4x + 1)(x - 5).

Workings out:

4x² + 20x + x - 5 = 4x² + 21x - 5

CORRECT ANSWER
4x² + 20x + x - 5
EDDIE SAYS
The sign in front of 20x is incorrect! 4x × -5 = -20x! The correct answer should read 4x² -19x - 5.
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