| Surviving College Algebra |
| "When all you want is the grade" |
 | |  | |  | |  |
| Multiplying Polynomials |
Multiplying monomials is rather simple. Use the distribution rule (remember a(b + c) = ab + ac?). It is this idea that will apply to larger
problems. There is one main rule to
remember- Multiply every term in one by
every term in the other!
Example
3
(4 + b - c)
Multiply
the 3 by everything in parentheses.
12
+ 3 b –3c
Write
it in the correct order.
3 b
– 3 c + 12
Answer!
Example
-2(4
– 5x)
Multiply
–2 by everything.
-8
+ 10x
Write
it in the correct order.
10
x – 8
Answer!
Example
(4
– 3 x) (2 + x)
This
is a harder problem but the same rule still applies. Look at the first polynomial, (4 – 3 x),
multiply every term in it, the 4 and –3x, by every term in the other one, the 2
and x. The best way to do this is to go
from left to right. Start with the 4 and
multiply it by the 2 and then the x . 4*2 + 4*x= 8 + 4x.
4
(2 + x) = 8 + 4 x
Take
the –3x and multiply by 2 + x.
-3
x (2 + x) = - 6 x – 3 x 2
Write
out the results.
8 +
4 x – 6x - 3x 2
Write
in correct order (highest exponent to lowest) and combine the like terms (4 x –
6x = -2x).
3x 2
– 2x + 8
Answer!
Example
(y 2 – 2y –3)(y – 4)
Remember
the rule, multiply every term in one (y 2 – 2y –3), by every term in
the other (y – 4). The first thing is to multiply y 2 by (y – 4)
then –2y by (y – 4) and last –3 by (y - 4).
y
2 (y – 4)= y 3 – 4y2
-2
y (y – 4) = - 2 y2 + 8 y
-3
(y – 4) = -3 y + 12
Write
out all the results.
y 3 –
4y2- 2 y2 + 8 y - 3 y + 12
Combine
like terms and write in correct order.
y 3 –
6y2 + 5 y + 12
Answer!
Example
(x 2 – 2x –3)(x 3
+ 5 x)
Multiply
ever term in one (x 2 – 2x –3) by every term in the other (x 3
+ 5 x). This means to multiply x 2 by
x 3 and 5 x.
x
2 (x 3 + 5 x) = x 5
+ 5x 3
Multiply
–2x and –3 by x 3 and 5 x.
- 2
x (x 3 + 5 x) = -2x 4 - 10x 2
-3
(x 3 + 5 x) = -3 x 3 - 15x
The
first step is now done, write all of the results on
the same line.
x
5 + 5x 3-2x 4 - 10x 2 - 3 x 3
- 15x
Combine
like terms.
x
5 -2x 4 + 2x 3- 10x 2 - 15x
Answer!