Page 42 - 新思维数学学生用书8 样章

2.3 Expanding brackets

Summary checklist

I can substitute numbers into expressions.
I can write formulae.

I can understand and use formulae.
I can change the subject of formulae.

2.3 Expanding brackets

In this section you will … Key word

• expand brackets. expand brackets

To expand brackets, multiply each term inside the brackets by the term

directly in front of the brackets.

Tip

Expanding brackets is sometimes called multiplying out

brackets.

Worked example 2.3

a Expand these expressions. i 3(2b + 5) ii a(a − 3)
b Expand and simplify this expression. 4(2x + 3x ) − x(6 + x)
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Answer

a i 3(2b + 5) = 3 × 2b + 3 × 5 Multiply 3 by 2b then multiply 3 by 5.
= 6b + 15 Simplify 3 × 2b to 6b and simplify 3 × 5 to 15.
ii a(a − 3) = a × a − a × 3 Multiply a by a then multiply a by −3.
= a − 3a Simplify a × a to a and simplify a × −3 to −3a.
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b 4(2x + 3x ) − x(6 + x) Start by multiplying out both brackets.
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= 8x + 12x − 6x − x 2 So, 4 × 2x = 8x, 4 × 3x = 12x , −x × 6 = −6x, −x × x = −x 2
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= 2x + 11x 2 Collect like terms: 8x − 6x = 2x and 12x − x = 11x .
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