Identify the like terms: 3x + 5x Add the coefficients: 3x + 5x = (3 + 5)x State the answer: 8x Answer: 8x

Identify the like terms: 7a - 2a Subtract the coefficients: 7a - 2a = (7 - 2)a State the answer: 5a Answer: 5a

Rewrite the lone term: 9y - 1y Subtract the coefficients: (9 - 1)y State the answer: 8y Answer: 8y

Simplifying and single brackets Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Simplifying and single brackets questions. See exactly how to solve problems on collecting like terms, two variables, constants, multiplying terms.

collecting like termstwo variablesconstantsmultiplying termsindicesexpanding brackets

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Simplify

3x + 5x

Worked solution

Identify the like terms
$3x + 5x$
Both terms contain the letter x, so they are like terms.
Add the coefficients
$3x + 5x = (3 + 5)x$
Add the numbers in front of x: $3 + 5 = 8$ .
State the answer
$8x$
The simplified expression is 8x.

Answer

8x

Question 2

1 markeasy

Simplify

7a - 2a

Worked solution

Identify the like terms
$7a - 2a$
Both terms contain a, so they can be combined.
Subtract the coefficients
$7a - 2a = (7 - 2)a$
$7 - 2 = 5$ , keeping the letter a.
State the answer
$5a$
The simplified expression is 5a.

Answer

5a

Question 3

1 markeasy

Simplify

4x + 2x + x

Worked solution

Count the x terms
$4x + 2x + 1x$
A lone x means 1x.
Add the coefficients
$(4 + 2 + 1)x$
$4 + 2 + 1 = 7$ .
State the answer
$7x$
The simplified expression is 7x.

Answer

7x

Question 4

1 markeasy

Simplify

9y - y

Worked solution

Rewrite the lone term
$9y - 1y$
Subtracting y means subtracting 1y.
Subtract the coefficients
$(9 - 1)y$
$9 - 1 = 8$ .
State the answer
$8y$
The simplified expression is 8y.

Answer

8y

Question 5

2 markseasy

Simplify

6a + 3b + 2a + 4b

Worked solution

Group the a terms and the b terms
$(6a + 2a) + (3b + 4b)$
Keep a terms with a terms and b terms with b terms.
Add each group
$8a + 7b$
$6a + 2a = 8a$ and $3b + 4b = 7b$ .
State the answer
$8a + 7b$
The a terms and b terms cannot be combined, so the answer is 8a + 7b.

Answer

8a + 7b

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