Game Development Reference
In-Depth Information
Here is another problem that appears involved until you rearrange its terms so
that you can view them in relative isolation:
2
x
2
y
3
z
6
x
3
y
5
z
3
8
x
1
y
4
z
5
10
x
2
y
3
ð
2
8
Þðx
2
x
1
Þðy
3
y
4
Þz
1
z
5
Group like terms
:
ð
6
10
Þðx
3
x
2
Þðy
5
y
3
Þðz
3
Þ
16
x
2
þ
1
y
3
4
z
1
5
60
x
3
þ
2
y
5
þ
3
z
3
Perform multiplications
:
16
x
3
y
1
z
4
60
x
5
y
8
z
3
Simplify
:
x
3
x
5
y
1
y
8
z
4
z
3
16
60
Group like terms
:
4
15
x
3
5
y
1
8
z
4
ð
3
Þ
Perform divisions
:
4
15
x
2
y
9
z
1
:
Simplify
4
15
x
2
y
9
z
1
Remove negative exponents
:
To work with this problem, you proceed in two distinct phases. For the first
phase, you group like terms and carry out the multiplications. For the second
phase, you again group like terms, but this time you carry out the divisions.
Monomial and Binomial Expressions
As emphasized previously, the distributive property proves important when
carrying out multiplication operations. When you multiply a polynomial by an
expression consisting of only one term, you apply the single term to each of the
terms in the polynomial expression. Here is an example:
3
xð
4
x þ
2
Þ
ð
3
xÞð
4
xÞþ
3
xð
2
Þ
3
x
applied to both of the terms in the binomial
:
12
x
2
þ
6
x
Completing the multiplications
:
