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May 25th

May 25th

# Multiplying Polynomials

After studying this lesson, you will be able to:

• Multiply polynomials.

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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