Page 47 - 新思维数学学生用书7 样章

2 Expressions, formulae and equations

2.4 Expanding brackets

In this section you will … Key words

• expand brackets. brackets

expand
Some algebraic expressions include brackets.
To expand a term with brackets, you multiply each term inside the brackets Tip

by the term outside the brackets. Expanding a term with brackets is
sometimes called ‘expanding the brackets’ or ‘multiplying out the brackets’. 4(n + 3) means
4 × (n + 3), but
you usually write
an expression
Worked example 2.4 like this without

Expand the brackets. the ×.
a 4(n + 3) b 2(x − 5) c 3(2g + h − 7)

Answer

a 4(n + 3) = 4 × n + 4 × 3 Multiply the 4 by the n, then multiply the 4 by
the 3.
= 4n + 12 Simplify the 4 × n to 4n and simplify the 4 × 3 to
12. Add the two terms together.
b 2(x – 5) = 2 × x − 2 × 5 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 − 7) = 3 × 2g + 3 × h − 3 × 7 The first term is 3 × 2g, which is the same as
3 × 2 × g, which simplifies to 6g.
= 6g + 3h − 21 There are three terms. You need to add the first
two terms and then subtract the third term.

Exercise 2.4

1 Copy and complete the following. Expand the brackets first.

a 2(x + 9) = 2 × x + 2 × 9 b 3(y − 1) = 3 × y − 3 × 1

= 2x + = 3y −
c 47 + p ) = 4 × 7 + 4 × p d 5(q − 3) = 5 × q − 5 × 3
(
= + = −

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