Page 27 - 新思维数学活动用书9 样章

2 Expressions and formulae

Practice

6 Expand and simplify each expression.
a (x + 5)(x + 2) b (x + 4)(x − 2) c (x − 6)(x + 3)
d (x − 3)(x − 3) e (x + 5)(x + 10) f (x − 5)(x − 8)

g (x − 5)(x + 10) h (x + 5)(x − 8)
7 Which answer is correct, A, B or C?
a (w + 7)(w + 8) = A w + 15w + 15 B w + 15w + 56 C w + w + 56
2
2
2
b (x + 5)(x − 3) = A x + 2x − 15 B x − 8x − 2 C x + 8x − 15
2
2
2
c (y − 6)(y + 4) = A y − 10y − 2 B y − 2y − 2 C y − 2y − 24
2
2
2
d (z − 3)(z − 5) = A z − 2z + 8 B z + 8z − 15 C z − 8z + 15
2
2
2
8 This is part of Rohan’s homework.
He has made a mistake in every question.
Question
Expand and simplify each expression.
1 (x + 4)(x + 3)
2 (x + 5)(x – 9)

3 (x – 3)(x – 2)
Answer
1 x + 4x + 3x + 7 = x + 7x + 7
2
2
2 x + 5x – 9x – 45 = x + 4x – 45
2
2
3 x – 2x – 3x – 6 = x – 5x – 6
2
2

Explain the mistakes Rohan has made and write the correct solutions.
9 a Expand and simplify each expression.
i (a + 2) 2 ii (a − 2) 2 iii (b + 4) 2
iv (b − 4) 2 v (c + 1) 2 vi (c − 1) 2
b Compare your answers to i and ii, iii and iv, v and vi.
What is the same and what is different about your answers to each pair of expansions?

c Use your answer to part b to copy and complete this general expression:
(x + y) = x + 2xy + y so (x − y) = …………………………
2
2
2
2

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