Easy Algebra Step-by-Step

Multiplying Polynomials 101

Step 4. State the main result.

()xy+ =()xyx+ ()xy+ =+xxxyy+

(^222)

• 2 +

Multiplying Polynomials

Multiplying Two Polynomials

To multiply two polynomials, multiply all the terms of the second polynomial

by each term of the fi rst polynomial and then simplify.

Problem Find the product.

a. ()))()((^2

b. ()^22 )))()(((

c. ()))))(((()(^2

Solution

a. ()))()((^2

Step 1. Multiply all the terms of the second polynomial by each term of the

fi rst polynomial.

() 21 x (^1) () 353 x^2555 xx+ 444 2222 xx⋅ 323 xx^222 x⋅ 52 xx 222 x⋅ 411 ⋅ 31 xx^21115151 ⋅ 4
= 6 xx^3211111000008 xx 33533 2 x− 4
Step 2. Simplify.
= 61 xxx^32 − 1133131 ++ 343 −
b. ()^22 )))()(((
Step 1. Multiply all the terms of the second polynomial by each term of the
fi rst polynomial.
()^4 xx^222222 x−^55 ()^22 xx^2 x−^3
= 42 xx^22 ⋅ 22 − 44 xx^22 ⋅ − 4 xx⋅ 3232 ++ ⋅ 22 xx^22 − 22 ⋅xx− 22323 ⋅ − 5252 ⋅ xx++ 555 ⋅ + ⋅ 3
= 84 xx^43 − 44 −+ 12 x^23 + 4426 xxxxx−− 262 226 −+ 1010 + 515 + 5
Step 2. Simplify.
= 82 xx^42 − 224414 −+x 5
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