Page 86 - Cambridge+Checkpoint+Mathematics+Coursebook+9

9.1 Simplifying algebraic expressions

9.1 Simplifying algebraic expressions

You already know how to use the laws of indices for multiplication and division of numbers.
You can also use these rules with algebraic expressions.

When you multiply powers of the same variable, you add the indices. x × x = x
a + b
a
b
When you divide powers of the same variable, you subtract the indices. x ÷ x = x
a − b
a
b
Worked example 9.1
7
2
3
3
4
Simplify each expression. a x × x b y ÷ y c 2m × 8m d 12b 9
3
6b 8
3
2
a x × x = x 2 + 3 To multiply, add the indices.
= x 2 + 3 = 5, so the answer is x .
5
5
7
b y ÷ y = y 7 − 4 To divide, subtract the indices.
4
3
3
= y 7 − 4 = 3, so the answer is y .
3
3
c 2m × 8m = 2 × 8 × m 3 + 3 Multiply the 2 by the 8, to simplify the numbers, and add the indices
= 16m 6 as normal. 2 × 8 = 16, 3 + 3 = 6, so the answer is 16m .
6
−
d 12b 9 = 12 × b 98 Divide the 12 by the 6, to simplify the numbers, and subtract the
6b 8 6 indices as normal.
1
= 2b 12 ÷ 6 = 2, 9 − 8 = 1, so the answer is 2b . Write this as 2b.
) Exercise 9.1
1 Simplify each expression.
a x × x b y × y c z × z d m × m e n × n f p × p
7
2
4
9
8
6
3
6
3
4
5
g q ÷ q h r ÷ r i t ÷ t j u ÷ u k v ÷ v l w ÷ w
2
3
4
8
7
6
6
8
7
8
9
2 Simplify each expression.
a 3x × 2x b 4y × 3y c 6z × 5z d 2m × 2m e 4n × n f p × 8p
2
3
5
2
3
6
7
4
5
2
4
g 6q ÷ 2q h 9r ÷ 3r i 15t ÷ 5t j 8u 7 k 2v 6 l 5w 7
6
7
5
9
10
3
4u 2 v 2 w 6
3 Which answer is correct, A, B, C or D?
a Simplify 2e × 3e . A 5e B 6e C 5e D 6e 6
2
8
4
8
6
b Simplify 3g × 5g. A 15g B 15g C 8g D 8g 7
7
6
6
6
c Simplify 10k ÷ 5k . A 5k B 5k C 2k D 2k 4
2
4
6
8
6
2
2
d Simplify 8m 2 . A 6m B 6m C 4m D 4m
2m
4 Here are some algebra cards.
4
5
4x × 2x
8
12x ÷ x 2
3
2x × 3x 12x ÷ 2x
10
3
3
8x × x 6x × 2x
3
6
3
3x × 4x 3
2
a Separate the cards into two groups. Explain how you decided which group to put them in.
b Which card does not fit into either of the groups? Explain why this is.
9 Expressions and formulae 85