Basic Mathematics for College Students

Caution! A common error when squaring a binomial is to square only its

first and second terms. For example, it is incorrect to write

The correct answer is 25x^2  40 x16.

Multiply polynomials.

To develop a general rule for multiplying any two polynomials, we will find the
product of and. In the solution, the distributive property is used
four times.

Distribute.

Distribute.

Multiply the monomials.

 6 x^3  15 x^2  19 x 15 Combine like terms.

 6 x^3  9 x^2  6 x^2  9 x 10 x 15

(2x) 3 x^2 (3) 3 x^2 (2x) 3 x(3) 3 x(2x) 5 (3) 5

(2x3) 3 x^2 (2x3) 3 x(2x3) 5

(2x3) 3 x^2 (2x3) 3 x(2x3) 5

(2x3)(3x^2  3 x5)

2 x 3 3 x^2  3 x 5

4

 25 x^2  16

15 x 422  15 x 22  1422

Appendix II Polynomials A-17

Self Check 3

Multiply:

a.

b.

Now TryProblems 35 and 39

(2a1)(3a2)

(y3)(y1)

Solution

a.

FO I L

Multiply the monomials.

Combine like terms.

b.

FOIL

Multiply the monomials.

 6 x^2 x 12 Combine like terms.

 6 x^2  9 x 8 x 12

(3x4)(2x3) 3 x(2x) 3 x(3)4(2x)4(3)

O

F

I L

x^2  12 x 35

x^2  7 x 5 x 35

(x5)(x7)x(x)x(7)5(x)5(7)

O

F

I L

EXAMPLE (^4) Find: (5x4)^2
StrategyWe will write the base, 5x4, as a factor twice, and perform the
multiplication.
WHYIn the expression (5x4)^2 , the binomial 5x4 is the base and 2 is the
exponent.
Solution
Write the base as a factor twice.
FO I L
Multiply the monomials.
 25 x^2  40 x 16 Combine like terms.
 25 x^2  20 x 20 x 16
 5 x(5x) 5 x(4)(4)(5x)(4)(4)
(5x4)^2 (5x4)(5x4)
O
F
I L
Self Check 4
Find: (5x4)^2
Now TryProblem 41