Game Development Reference
In-Depth Information
Figure 4.1
Factoring results in a product.
You are then in a position to group the common factors so that they reveal the
largest common factor:
½ð
1
Þð
2
Þð
7
Þa ½ð
1
Þð
2
Þð
2
Þð
2
Þ½ð
7
Þ
If you carry out the implied multiplication, you arrive at the largest common
factor for the two terms:
ð
14
Þa ð
14
Þð
2
Þð
2
Þ¼
14
a
14
ð
4
Þ¼
14
ða
4
Þ
One of the key notions in factoring is that when you factor an expression, you
end up with a product. As Figure 4.1 illustrates, factoring two expressions results
in a new expression that implies that a multiplication can take place. Generally,
then, you have successfully factored an expressionwhen you rewrite it as a product.
Given that you factor a term, you can then check the correctness of your activities
if you carry out the implied multiplication:
14
ða
4
Þ¼
14
a
56
A further extension of factoring involves collecting like terms. If an expression
contains terms that are exactly alike, then you can rewrite the expression so that
you use one instead of several instances of the like term in the expression. As in
previous examples, when you collect like terms, you create a product. As
examples of expressions possessing collectable terms, consider the following:
8
c þ
6
c ¼ð
8
þ
6
Þc ¼
14
c
7
a
2
þ
5
a
2
þ
6
a
3
3
a
3
¼ð
7
þ
5
Þa
2
þð
6
3
Þa
3
¼
12
a
2
þ
3
a
3
¼
3
ð
4
a
2
þ a
3
Þ
In the first example,
c
is common to both terms, so you can use the distributive
property to factor the sum of 8 and 6 into a single expression that you can
multiply by
c
. After you regroup the integers, you can carry out the addition and
arrive at a single term, 14
c
.
