Page 26 - 新思维数学活动用书9 样章

2.4 Expanding the product of two linear expressions

3 Use the same method as in Question 2 to expand these brackets. Tip
The first one has been done for you. Take care with
a (x + 5)(x − 3) b (x + 6)(x − 2) the minus signs.
× x +5 × x +6

x x 2 +5x x x 2
−3 −3x −15 −2

Answer: x + 5x − 3x − 15 Answer: x + − −
2
2
= x + 2x − 15 = x + −
2
2
c (x − 7)(x + 4) d (x − 8)(x + 2)
× x −7 × x −8

x x 2 x
+4 +2

Answer: x − + − = Answer: x − + −
2
2
x − − = x − −
2
2
4 Use the same method as in Question 2 to expand these brackets. Tip
The first one has been started for you.
a (x − 1)(x − 3) b (x − 4)(x − 8) Take care with
the minus signs.
× x −1 × x −4
x x 2 −1x x
−3 −3x +3 −8

Answer: x − − + 3 Answer: x − − +
2
2
= x − + = x − +
2
2
5 In questions 2, 3 and 4, you used a multiplication grid to expand two
brackets.
Do you prefer to use the arc method shown here?

2
(x + 8 )(x − 4 ) = x − 4 x + 8 x −32

= x + 4 x −32
2
Or do you prefer the multiplication grid method shown here?
× x +8
x x 2 +8x

−4 −4x −32

= x + 8x − 4x − 32 = x + 4x − 32
2
2
Or do you prefer a different method? Explain your answer.

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