Easy Algebra Step-by-Step

Multiplying Polynomials 95

Solution

a. ()^53 y )()(^26 y

Step 1. Multiply the numerical coeffi cients.

()^5 ()^3 =^15

Step 2. Multiply the variable factors.

()xy^53 ()xy^26 =x^7 y^9

Step 3. Use the product in step 1 as the coeffi cient

of xy^79.

()^5 xy^53 ()^3 xy^26 =^15 xy^79

b. ()^343 )()( b^2

Step 1. Multiply the numerical coeffi cients.

()− )()( =−^16

Step 2. Multiply the variable factors.

()ab^34 b ()ab^2 =ab^46

Step 3. Use the product in step 1 as the coeffi cient of ab^46 b.

()− )()( )=−^1616 ab^446

c.())))()(((

Step 1. Multiply the numerical coeffi cients.

())()( )=− 12

Step 2. Multiply the variable factors.

()x()x =x^2

Step 3. Use the product in step 1 as the coeffi cient of x^2.

() 6 x() 22 x =− 12 x^2

d. ()^32 )))()(((

Step 1. Multiply the numerical coeffi cients.

() 10 )(() 44 ))=− 0

To streamline your work when

you are multiplying polynomials,

arrange the variables in each term

alphabetically.

Recall from Chapter 7 that

when you multiply exponential

expressions that have the same

base, you add the exponents.

If no exponent is written on

a variable, the exponent is

understood to be 1.