KS3 Maths · Year 7 · Chapter 10: Algebra · Lesson 3

Expanding brackets

Year 7About 60 minutesNo calculator49 marks

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Quick questions to start.

A1
Needed today
Work out $- 6 \times - 7$ .
[1 mark]
Answer
A2
Last lesson
Simplify $7 p + 3 q - 2 p - 5 q$ .
[1 mark]
Answer
A3
From chapter 8
Write $6.2 \times 1 0^{3}$ as an ordinary number.
[1 mark]
Answer
A4
From chapter 4
Increase $40$ by $25%$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Expand the brackets.

(a) $5 (x + 3)$ (b) $4 (2 y - 7)$

Hint Multiply every term inside the bracket by the number outside.

B1
Expand the brackets.
(a) $3 (k + 8)$ (b) $7 (2 m - 3)$
(c) $4 (5 p + 3 q)$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 2

Expand the brackets.

(a) $- 2 (x + 6)$ (b) $- 4 (3 y - 5)$

Hint The

- 2

multiplies both terms. A negative times a negative is positive:

- 4 \times - 5 = + 20

B2
Expand the brackets.
(a) $- 5 (t + 4)$
(b) $- 3 (2 w - 9)$
(c) $- (6 - n)$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 3

Expand the brackets.

(a) $x (x + 9)$ (b) $3 y (2 y - 5)$

Hint

x \times x = x^{2}

, and

3 y \times 2 y = 6 y^{2}

B3
Expand the brackets.
(a) $a (a - 6)$ (b) $4 t (3 t + 2)$
(c) $2 k (7 - 3 k)$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 4

Expand and simplify $3 (2 x + 5) + 4 (x - 2)$ .

Hint Expand each bracket first. Then collect the

x

terms and the numbers.

B4
Expand and simplify.
(a) $5 (y + 3) + 2 (3 y - 4)$
(b) $2 (4 a - b) + 3 (a + 2 b)$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 5

Expand and simplify $6 (x + 2) - 3 (x - 4)$ .

Hint The

- 3

multiplies both terms in the second bracket:

- 3 \times - 4 = + 12

B5
Expand and simplify.
(a) $4 (2 m + 5) - 3 (m + 2)$
(b) $7 (n - 1) - 2 (3 n - 5)$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Practice

Year 7

C1
Write $98$ as $100 - 2$ . Use a bracket to work out $6 \times 98$ without a calculator. Show your method.
[2 marks]
Answer $\dots\dots$
C2
Write down the missing numbers.
(a) $4 (x + 000) = 4 x + 28$
(b) $000 (3 y - 2) = 15 y - 10$
[2 marks]
Answer(a) $\dots$ (b) $\dots$

C3
Expand $\frac{1}{2} (6 x - 10)$ .
[1 mark]
Answer
C4
Expand $3 (2 a - 4 b + 5)$ .
[1 mark]
Answer
C5
Write an expression for the area of this rectangle. Do not use brackets in your answer.
[2 marks]
Not drawn accurately
Answer $\dots\dots cm^{2}$
C6
Expand and simplify $x (x + 4) + 3 x (x - 2)$ .
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Mia says, " $2 (x + 5) = 2 x + 5$ ."
Mia is wrong. Explain why, and write down the correct expansion.
[2 marks]

D2
Show that $3 (2 x + 4) - 2 (x - 3)$ simplifies to $2 (2 x + 9)$ .
[3 marks]
D3
The diagram shows two rectangles, $A$ and $B$ .
Not drawn accurately
(a)
Show that the total area of the two rectangles is $(10 x + 21)$ cm².
[3 marks]
(b)
The total area is $71$ cm². Work out the value of $x$ .
[2 marks]
Answer $x = \dots\dots$
Total for D3: 5 marks
D4
An adult ticket costs $£ (x + 4)$ and a child ticket costs $£ x$ . The Lee family buys $2$ adult tickets and $3$ child tickets. The Shah family buys $3$ adult tickets and $1$ child ticket.
(a)
Write an expression, in pounds, for what the Lee family pays. Simplify it.
[2 marks]
Answer $£ \dots\dots$
(b)
Show that the Lee family pays $£ (x - 4)$ more than the Shah family.
[2 marks]
Total for D4: 4 marks
D5
Expand and simplify
(a)
$5 (2 p - 3) - (p - 7)$
[2 marks]
Answer
(b)
$2 y (y + 3) - y (y - 4)$
[2 marks]
Answer
Total for D5: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
$a$ and $b$ are whole numbers, and
$a (x + 3) + b (x - 1) = 7 x + 9$
for every value of $x$ . Work out $a$ and $b$ .
[4 marks]
Hint 1 · What to try
Expand the left side: $a x + 3 a + b x - b$ .
Hint 2 · The first line
The $x$ terms give $a + b = 7$ . The numbers give $3 a - b = 9$ .
Hint 3 · The full method
Add the two: $4 a = 16$ , so $a = 4$ . Then $b = 7 - 4 = 3$ .
Answer $a = \dots\dots$ $b = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can expand a bracket with a number or a negative number outside.
I can expand a bracket with a letter outside, such as $x (x + 9)$ .
I can expand two brackets and collect like terms.
I can use brackets in areas and costs.

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