Page 101 - Mathematics Coursebook

9.2 Expanding brackets

9.2 Expanding brackets

Some algebraic expressions include brackets.
To expand a term with brackets, you multiply each term inside the 4(n + 3) means 4 × (n + 3), but you
usually write an expression like this
brackets by the term outside the brackets. Expanding a term with without the multiplication sign.
brackets is sometimes called expanding the brackets or multiplying
out the brackets.

Worked example 9.2

Expand the brackets.
a 4(n + 3) b 2(x − 5) c 3(2g + h)

a 4(n + 3) = 4 × n + 4 × 3 Multiply the 4 by the n then the 4 by the 3.
= 4n + 12 Simplify the 4 × n to 4n and the 4 × 3 to 12.
b 2(x − 5) = 2 × x − 2 × 5 This time there is a minus sign before the 5,
= 2x − 10 so you need to take away the 10 from the 2x.
c 3(2g + h) = 3 × 2g + 3 × h The fi rst term is 3 × 2g, which is the same as 3 × 2 × g
= 6g + 3h which simplifi es to 6g.

) Exercise 9.2

1 Expand the brackets.
a 2(x + 5) b 3(y + 6) c 4(w + 2) d 5(z + 5)
e 3(b − 1) f 7(c − 4) g 6(d − 9) h 2(e − 8)
i 6(2 + f ) j 2(1 + g) k 5(7 + h) l 9(3 + i)
m 6(2 − x) n 2(1 − y) o 5(7 − p) p 9(3 − q)

2 Multiply out the brackets.
a 3(2x + 1) b 4(3y + 5) c 5(2w + 3) d 6(4z + 7)
e 2(3b − 4) f 4(2c − 3) g 6(5d − 1) h 8(3e − 6)
i 3(1 + 2f ) j 5(3 + 4g) k 7(6 + 7h) l 9(5 + 4i)
m 8(3 − 5x) n 12(2 − 3y) o 6(5 − 8p) p 2(13 − 4q)
3 This is part of Bethan’s homework.
Bethan has made a mistake on Question Multiply out the brackets.
every question. a 4(x + 4) b 2(6x – 3)
Explain what Bethan has done c 3(2 – 5x) d 6(2 – x)
wrong. Solution
a 4(x + 4) = 4x + 8 b 2(6x – 3) = 12x – 3
4 Which one of these expressions is
different from the others? c 3(2 – 5x) = 6 + 15x d 6(2 – x) = 12 – 6x = 6x
Explain your answer.

2(12x + 15) 6(5 + 4x)
3(10 + 8x) 4(6x + 26)

100 9 Expressions and equations