Page 39 - 新思维数学学生用书9 样章

2 Expressions and formulae

Exercise 2.4

1 Copy and complete these multiplications.

a (x + 4)(x + 1) = x + 1x + x + b (x − 3)(x + 6) = x + 6x − x −
2
2
= x + x + = x + x −
2
2

c (x + 2)(x − 8) = x − x + x − d (x − 4)(x − 1) = x − x − x +
2
2
= x − x − = x − x +
2
2
2 Expand and simplify.
a (x + 3)(x + 7) b (x + 1)(x + 10)
c (x + 5)(x − 3) d (x − 4)(x + 8)

e (x − 7)(x − 2) f (x − 12)(x − 2)

Think like a mathematician

3 Sofia and Zara discuss the different methods they use to expand two brackets.
Read what they say.

This is the
method I use:
I use the same (x + 4)(x + 1)
method as in = x(x + 1) + 4(x + 1)
Question 1. = x + x + 4x + 4
2
= x + 5x + 4
2

a Critique Zara’s method. Do you prefer Zara’s method or Sofia’s method?
Why?

b Can you think of another method you can use to expand two brackets?
c Discuss your answers to parts a and b with other learners in your class.

4 Expand and simplify these expressions. Use your favourite method.
a (y + 2)(y + 4) b (z + 6)(z + 8)

c (m + 4)(m − 3) d (a − 9)(a + 2)
e (p − 6)(p − 5) f (n − 10)(n − 20)

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