Page 100 - Mathematics Coursebook

9.1 Collecting like terms

3 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 b 12p 12p Start by working
Start by working
5x + x = 6x
out 12p – 8p
6x 6x 8p 8p out 12p – 8p
3x 3x 5x 5x x x 7p 7p

4 Simplify these expressions by collecting like terms.
a 2a + 3a + 5b b 3c + 5c + 2d + d c 4x + 5y + 3x + 2y
d 7h + 8g + 2h + g e 4t + 1 + 3t + 9 f 6m − 2m + 7n − 3n
g 10q − 5q + 17 − 9 h 6t + 3v − 4t + v i 9k + 5f − 3k − 2f
j 7r + 2s + 3t − 2r + s + 2t k 11q + 6y + 9 − 3y − 7 l 12 + 6h + 8k − 6 − 3h + 3k

5 Write each expression in its simplest form.
The first one is done for you. 2ab and 3ab are like terms so you can

a 2ab + 3ab + 5pq + 7qp = 5ab + 12pq add them to give 5ab.
b 3st + 5st + 9pu + 7up c 4vb + 2bv + 6ad − 4da 7qp means 7 × q × p which is the same
d 11rt + 9gh − 2rt − 7hg e 8xy + 12xz + 3yx − 9zx as 7 × p × q, so 5pq and 7qp are
f 6a + 7ac − 2a + ac g 4mn − 3nm + 7gh − 7hg like terms. When you write your answer,

6 This is part of Dai’s homework. put the letters in alphabetical order, so
Dai has made several mistakes. write 12pq and not 12qp.
Explain what Dai has done wrong.

Question Write these expressions in their simplest form.
a 2x + 8 + 6x – 4 b 3bc + 5bd – 2bc + 3db
Solution a 2x + 8 + 6x – 4 = 8x + 4 = 12x
b 3bc + 5bd – 2bc + 3db = 5bc + 5bd + 3db

7 Copy and complete this algebraic pyramid.

Remember, you fi nd the expression
in each block by adding the expressions
in the two blocks below it.
12c + 11d

7c + 3d
2c + 6d
c + d

9 Expressions and equations 99