Intermediate Algebra (11th edition)

Multiplying Polynomials Vertically

Find each product.

(a)

Write the factors vertically.

Multiply

Multiply

Combine like terms.

(b)

Combine like terms.

NOW TRY

9 m^4 - 21 m^3 + 10 m^2 + 12 m - 20

9 m^4 - 6 m^3 + 12 m 3 m 13 m^3 - 2 m^2 + 42

- 15 m^3 + 10 m^2 - 20 - 513 m^3 - 2 m^2 + 42

3 m - 5

3 m^3 - 2 m^2 + 4

13 m^3 - 2 m^2 + 4213 m- 52

15 a^2 - ab- 2 b^2

15 a^2 - 6 ab 3 a 15 a- 2 b 2.

5 ab- 2 b^2 b 15 a- 2 b 2.

3 a + b

5 a - 2 b

15 a- 2 b 213 a+b 2

EXAMPLE 3

294 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

Be sure to

write like terms

in columns.

NOTE We can use a rectangle to model polynomial multiplication.

Example 3(a)

Label a rectangle with each term, as shown below on the left. Then put the product of

each pair of monomials in the appropriate box, as shown on the right.

bb

Add the four monomial products.

Same result as in Example 3(a)

OBJECTIVE 3 Multiply binomials.There is a shortcut method for finding the

product of two binomials.

Distributive property

Distributive property again

Multiply.

Before combining like terms to find the simplest form of the answer, we check the

origin of each of the four terms in the sum

6 x^2 + 9 x- 8 x-12.

= 6 x^2 + 9 x- 8 x- 12

= 3 x 12 x 2 + 3 x 132 - 412 x 2 - 4132

= 3 x 12 x+ 32 - 412 x+ 32

13 x- 4212 x+ 32

= 15 a^2 - ab- 2 b^2

= 15 a^2 + 5 ab- 6 ab- 2 b^2

15 a- 2 b 213 a+b 2

- 2 b - 2 b - 6 ab - 2 b^2

5 a 5 a 15 a^25 ab

3 a 3 a

15 a- 2 b 213 a+ b 2

NOW TRY
EXERCISE 3
Find the product.

t- 3

3 t^2 - 5 t+ 4

NOW TRY ANSWER

3. 3 t^3 - 14 t^2 + 19 t- 12