Adding and Subtracting Polynomials 91
Solution
a. ()^22 ))) ((()(((Step 1. Remove parentheses.()^9 xx^266666 x+^22 ()^77 xx^253555= 96 xx^22 − 66 ++ 2727 − xx− 535 +Step 2. Rearrange the terms so that like terms are together. (You might do
this step mentally.)
= 97 xxx^22 − 77 − 656 − x+ 23 +Step 3. Systematically combine matching like terms and
indicate addition or subtraction of unlike terms.
= 21 xx^2 − 1151 +Step 4. Review the main results.96 xx^22662727 xx 535 21 xx^21151()^9 xx^266666 x+^22 ()^77 xx^253555
= 9 + 22 55 = 2b. ()^32 ))))) (((()^3
Step 1. Remove parentheses.()^4 xx^3233333 x^2 −x+^88 ()^8888 xx^33 +^21 x^0
= 43 xx^32 +++ 33 −+xx+ 8888 ++^3 + 21 x− 0Step 2. Rearrange the terms so that like terms are together. (You might do
this step mentally.)
= 483 xx^33 +++ 8888 + xx^2 −− + 28 x+ − 10Step 3. Systematically combine matching like terms and indicate addition or
subtraction of unlike terms.
=+ 12 xx^32 ++ 3323 +−xStep 4. Review the main results.
38821012 34 3 238 8
(^323)
4 x xx xx 2
xx 3 x
()^48
xx^3233333 x^2 −x+ 8
()^8210
888 xx^33 + 21 x 100 444 x^3 + + 88 −=+ 12 x^3 +−x−− 2You should write
polynomial answers in
descending powers of a
variable.