Chapter 4 Algebra Worksheet Page 24
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501 9 9
4 D M U LT I P LY I N G A L G E B R A I C T E R M S
5
Simplify:
a
7a × 3c
b
−5p × 6
c
8n × 3n
2ef × 5gh
9xy × −2xz
3ab × 2d × 4f
d
e
f
−2gh × 5b × 7k
mn × 6m × 8q
4ab × 3ac × 2a
g
h
i
2
2
2
j
9m × np × 2m
k
7gh × −3gh × fgh
l
−2wx
× 5wy × −4u
6
Copy and complete these multiplication tables. Multiply each term in the left column
by each term in the top row.
2
×
×
a
4a
3
6m
2abc
b
3x
4xyz
−5y
2x
3d
−2x
2
2
ab
xy
5mn
6xy
2ac
−7yz
Copy and complete these multiplication problems. Each term is written in expanded
7
form fi rst.
3
4
3
4
2
× 2
× a
a
b
a
= 2 ×
×
× 2 ×
×
×
= a ×
×
× a ×
×
×
7
= 2
=
2
6
5
2
3
c
m
× m
d
x
× x
× x
= m ×
× m ×
×
×
×
×
= x ×
×
×
×
× x ×
× x ×
×
=
=
8
Look at your answers to question
7
. Can you see a shortcut that could be used?
Explain. This shortcut is known as one of the index laws.
EXAMPLE 4D-5
Multiplying terms in index form using an index law
Use an index law to simplify:
4
7
3
5
a
a
× a
b
b
× b × b
.
THINK
WRITE
4
7
1 Check the bases are the same (yes).
a
× a
a
a
11
2 Write the base and add the indices. (4 + 7 = 11)
= a
3
5
b
1 Check the bases are the same (yes).
b
b
× b × b
9
2 Write the base and add the indices. (3 + 1 + 5 = 9)
= b
Remember that b has an index or power of 1.
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