Page 48 - 新思维数学学生用书7 样章

2.4 Expanding brackets

2 Su and Li compare the methods they use to expand 6(x + 4).

Su uses a multiplication box like this: Li uses multiplication arcs like this:

× x + 4 6(x + 4) = 6x + 24
6 6x + 24
So 6(x + 4) = 6x + 24
So 6(x + 4) = 6x + 24

a Write down the advantages and disadvantages of Su’s method.
b Write down the advantages and disadvantages of Li’s method.
c Write down the advantages and disadvantages of the method used in Question 1.

d Which method do you think is best for expanding brackets correctly?
Explain why.
3 Expand the brackets.
a 3(y + 6) b 4(w + 2) c 5(z + 5) d 3(b − 1)

e 6(d − 9) f 2(e − 8) g 6(2 + f ) h 2(1 + g)
i 9(3 + i) j 6(2 − x) k 2(1 − y) l 5(7 − p)
4 Expand these brackets. Copy and complete the workings.
a 2 2x + 1) = 2 × 2x + 2 × 1 b 5 3( y − 2) = 5 × 3y − 5 × 2
(
= 4x + = 15y −

c 7 2g + 9 ) = 7 × 2g + 7 × 9p d 44q − 11 + ) r = 4 × 4q − 4 × 11 + 4 × r
p
(
(
= + = − +
5 Multiply out the brackets.
a 3(2x + 1) b 4(3y + 5) c 5(2w + 3) d 6(4z + 7v + 9)
e 2(3b − 4) f 4(2c − 3) g 6(5d − 1) h 8(3e − 6 + 2f )

i 3(a + 2f ) j 5(3b + 4g) k 7(6c − 7h) l 9(5 + 3h − 4i)

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