Page 44 - 新思维数学学生用书7 样章

2.3 Collecting like terms

3 Simplify each of these expressions.

a x + x + x + x + x b 2y + 4y c 5d + 3d
d 6t + 3t + 4t e 8g + 5g + g f 9p + p + 6p
g 7w − 4w h 8n − n i 9b − 5b 2
2
j 6f + 2f − 3f k 9j + j − 7j l 8k − 5k − 2k 3
3
3
4 In an algebraic pyramid, you find the expression in each block by adding the expressions in the
two blocks below it.
Copy and complete these pyramids.
a

5x+x=6x
6x

3x 5x x
b
12p Start by working
out 12p –8p
8p

7p

5 Copy and complete the workings to simplify these expressions.
a 2x + 8x + 6y + 9y = 10x + y
b 9d − 7d + 3h − h = d + 2h

c 2g + 8 + 3g – 5 = 2g + 3g + 8 – 5 = g +
d 8p + 12t − 3p + t = 8p − 3p + 12t + t = p + t
e 3a + 4b + 5c − 2b − 8c = 3a + 4b − 2b + 5c − 8c = a + b − c
6 Simplify these expressions by collecting like terms.
a 2a + 3a + 5b b 3c + 5c + 2d + d c 4t + 1 + 3t + 9

d 6m − 2m + 7n − 3n e 9k + 5f − 3k − 2f f 10q − 5q + 17 − 9
g 7r + 2s + 3t − 2r + s + 2t h 12 + 6h + 8k − 6 − 3h − 3k

Think like a mathematician

7 In pairs or groups, discuss what the terms xy and yx mean.
Also discuss how you can simplify these expressions:
a 4xy + 3yx b 8pq + 2ed − 3qp + 2de

What can you say, in general, about terms that have the same letters but are in a
different order?

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