February 8th
February 8th
Multiplying Polynomials
After studying this lesson, you will be able to:
When multiplying polynomials, we multiply the coefficients and
we add the exponents. If we have parentheses, we use the
distributive property.
Example 1
5a (3a 2 + 4)
We need to distribute 5a. Remember to multiply the
coefficients and add the exponents
15a 3 + 20a
Example 2
2m 2 (5m 2 - 7m + 8)
We need to distribute 2m 2 . Remember to multiply
the coefficients and add the exponents.
10m 4 - 14m 3 + 16m 2
Example 3
We need to distribute 2 3 x . Remember to multiply the
coefficients and add the exponents.
To multiply  by 12 x...we can do 2x times 12x and then
divide by 3 to get 8x 2
To multiply by -9...we can do 2x times -9 and then
divide by 3 to get -6x.
8x 3 - 6x
Example 4
-3x 2 y ( 2x 2 y- 3x y 2 - 7y
3 )
We need to distribute -3x 2 y. Remember to multiply
the coefficients and add the exponents.
-6x 4 y 2 + 9x 3 y 3 +
21x 2 y 4
Example 5
We need to distribute  . Remember to multiply the coefficients and add the
exponents. Remember that -y is the same as -1y.
Multiply -y times 20y 2 then divide by 2 to get
-10y 3.
Multiply -y times -10y then divide by 2 to get 5y 2
.
Multiply -y times 4 then divide by 2 to get -2y.
-10y 3 + 5y 2 -2y
Example 6
5x 2 (x + 7) - 2x (5x 2 - 3x + 7) + 2(x
3 - 8)
We have to distribute three times on this problem. Doing so
will give us:
5x 3 + 35x 2 - 10x 3 + 6x
2 - 14x + 2x 3 - 16
Now, we add like terms and put the terms in descending order:
-3x 3 + 41x 2 - 14x - 16
Example 7
Solve x(x - 3) + 4x - 3 = 8x + 4 + x (3 + x )
This is an equation. First we need to distribute to remove the
parentheses. This will give us:
x 2 - 3x + 4x - 3 = 8x + 4 + 3x + x 2
Next, we collect like terms on each side. This will give us:
x 2 + x - 3 = 11x + 4 + x 2
Next, we subtract x 2 from each side. This will
give us:
x -3 = 11x + 4
Now, we subtract x from each side to get: -3 = 10x + 4
Now, we subtract 4 from each side to get: -7 = 10x
Now we divided each side by 10 to get 
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