Game Development Reference
In-Depth Information
If you consider that the commutative and associate properties of numbers allow
you to express exponents in different ways, you can extend the work you perform
by grouping like terms. Consider this expression:
6
x
2
y
8
xy
3
6
8
x
2
x
1
y
1
y
3
:
Group like terms
48
x
3
y
4
Here is an example that incorporates negative exponents. While the grouping
creates a fraction, it still serves to simplify the terms:
2
xy
4
5
x
3
y ¼ð
2
5
Þðx
1
x
3
Þðy
4
y
1
Þ
¼
10
x
4
y
3
¼
10
x
4
y
3
Rewrite to make the negative
exponent positive
:
Using the distributive property, you can regroup like terms along the following
lines:
6
x
1
y
2
ð
3
x
4
5
xy
2
Þ
¼
6
x
1
y
2
ð
3
x
4
Þ
6
x
1
y
2
ð
5
x
1
y
2
Þ
Distribute the multiplications
:
¼
18
x
5
y
2
30
x
2
y
4
With this expression, you begin by using the distributive property to extract the
terms beginning with the coefficients 3 and 5 from the parentheses. You can then
group the resulting line terms and multiply the variables. To perform the mul-
tiplications, you add the exponents.
Note
You employ an exponent of 1 (x
1
) to make operations clearer. Normally, you do not need to use an
exponent of 1 because a number with an exponent of 1 equals itself (x ¼ x
1
).
Multiplication and Division Activities
When you approach situations in which you must divide one polynomial
by another, grouping like terms allows you to use the properties of expo-
nents more readily. Often, such work begins with expressions or terms that
