Game Development Reference
In-Depth Information
problem involving a binomial and a trinomial. You must multiply each term of
the first expression by each term of the second expression.
ðx
2
þ
3
x
4
Þð
2
x
2
þ
3
Þ
Trinomial and binomial
:
x
2
ð
2
x
2
þ
3
Þþ
3
xð
2
x
2
þ
3
Þ
4
ð
2
x
2
þ
3
Þ
Distribution
:
x
2
ð
2
x
2
Þþx
2
ð
3
Þþ
3
xð
2
x
2
Þþ
3
xð
3
Þ
4
ð
2
x
2
Þ
4
ð
3
Þ
Multiplying
:
2
x
4
þ
3
x
2
þ
6
x
3
þ
9
x
8
x
2
12
Collect terms
:
2
x
4
þ
6
x
3
þ
3
x
2
8
x
2
þ
9
x
12
Group like terms
:
2
x
4
þ
6
x
3
5
x
2
þ
9
x
12
:
Simplify
When you deal with polynomials that consist of several terms, you can use
approaches drawn from arithmetic. When you use such approaches, ordering the
terms in a polynomial by degree constitutes an important step. You can then
arrange the expressions in columns and carry out the multiplications. Here is an
example involving a trinomial and a binomial:
4
x
2
y
3
xy þ
2
y
xy þ
3
y
8
x
2
y
2
9
xy
2
þ
6
y
2
Multiply by the 3
y
:
3
x
3
y
2
3
x
2
y
2
þ
2
xy
2
Then multiply by
xy
:
3
x
3
y
2
5
x
2
y
2
7
xy
2
þ
6
y
2
Add the products
:
Exercise Set 8.3
Solve each equation.
a. 4x
5
4x
3
b. 3n
2
ð2n þ 3Þ
c. 2x
2
ð2x 2Þ
ð2z
2
þ 2Þð3z
2
d.
þ 4Þ
ð3t
2
3Þðt
2
e.
þ 2t þ 5Þ
f.
ða þ 4Þða þ 4Þ
g.
ð2a 1Þð3a þ 1Þ
