Page 45 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

9 Expand each expression and simplify by collecting like terms.

a x(x + 2) + x(x + 5) b z(2z + 1) + z(4z + 5)
c u(2u + 5) − u(u + 3) d w(6w + 2x) − 2w(2w − 9x)
10 This is part of Shen’s homework. He has made a mistake in every question.

Question

Expand and simplify
1 8(x + 5) – 3(2x + 7) 2 a(2b + c) + b(3c – 2a)
3 2y(y + 5x) + x(3x + 4y)

Answers
1 8(x + 5) – 3(2x + 7) = 8x + 40 – 6x + 21 = 2x + 61
2 a(2b + c) + b(3c – 2a) = 2ab + ac + 3bc – 2ab = ac + 3bc = 3abc 2
3 2y(y + 5x) + x(3x + 4y) = 2y + 10xy + 9x + 4xy = 9x + 2y + 14xy
2
2
2
2

a Explain what Shen has done wrong.
b Work out the correct answers.

Activity 2.3

Work with a partner to answer this question.
Here are six expressions.
A x(5x + 2) + 3x(4x + 1) B y(y + 4) + 6y (y + 8)
2
2
C 72pp + 7p − + 9p D 6k + 183 45k )
−
−
(
k
2
(
1)
2
E 5nn − 4) − 2nn + 2) F 8m ( m + 3) − 2m (4m − 3)
(
(
2
2
a Choose one of the expressions and ask your partner to expand the brackets
and simplify the expression. While they are working, you work out the answer
too.
Mark your partner’s work.
If your answers are different, discuss any mistakes that have been made.
b Now ask your partner to choose an expression for you.
Expand the brackets and simplify the expression.
Ask your partner to mark your work. Discuss any mistakes that have been made.
c Do this twice each, so four of the expressions have been chosen altogether.

Summary checklist

I can multiply out a bracket and collect like terms.

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