Adding and subtracting polynomials review

Adding and subtracting polynomials is all about combining like terms. In this article, we review some examples and give you a chance for you to practice the skill yourself.
Adding and subtracting polynomials is an exercise in combining like terms. Let's walk through some examples.

Example 1

Simplify.
left parenthesis, 5, h, start superscript, 3, end superscript, minus, 8, h, right parenthesis, plus, left parenthesis, minus, 2, h, start superscript, 3, end superscript, minus, h, start superscript, 2, end superscript, minus, 2, h, right parenthesis
Rewrite without parentheses:
start color blueD, 5, h, start superscript, 3, end superscript, minus, 8, h, end color blueD, start color maroonD, minus, 2, h, start superscript, 3, end superscript, minus, h, start superscript, 2, end superscript, minus, 2, h, end color maroonD
Group like terms:
left parenthesis, start color blueD, 5, h, start superscript, 3, end superscript, end color blueD, start color maroonD, minus, 2, h, start superscript, 3, end superscript, end color maroonD, right parenthesis, start color maroonD, minus, h, start superscript, 2, end superscript, end color maroonD, plus, left parenthesis, start color blueD, minus, 8, h, end color blueD, start color maroonD, minus, 2, h, end color maroonD, right parenthesis
Simplify:
3, h, start superscript, 3, end superscript, minus, h, start superscript, 2, end superscript, minus, 10, h
Want to see another example? Check out this video.

Example 2

Simplify.
left parenthesis, minus, w, start superscript, 3, end superscript, plus, 8, w, start superscript, 2, end superscript, minus, 3, w, right parenthesis, minus, left parenthesis, 4, w, start superscript, 2, end superscript, plus, 5, w, minus, 7, right parenthesis
Rewrite without parentheses (being careful to distribute the negative):
start color blueD, minus, w, start superscript, 3, end superscript, plus, 8, w, start superscript, 2, end superscript, minus, 3, w, end color blueD, start color maroonD, minus, 4, w, start superscript, 2, end superscript, minus, 5, w, plus, 7, end color maroonD
Group like terms:
start color blueD, minus, w, start superscript, 3, end superscript, end color blueD, plus, left parenthesis, start color blueD, 8, w, start superscript, 2, end superscript, end color blueD, start color maroonD, minus, 4, w, start superscript, 2, end superscript, end color maroonD, right parenthesis, plus, left parenthesis, start color blueD, minus, 3, w, end color blueD, start color maroonD, minus, 5, w, end color maroonD, right parenthesis, start color maroonD, plus, 7, end color maroonD
Simplify:
minus, w, start superscript, 3, end superscript, plus, 4, w, start superscript, 2, end superscript, minus, 8, w, plus, 7
Want to see another example? Check out this video.

Example 3

Express E, plus, F as a trinomial.
E=6c22c1F=4c2+7c+5\begin{aligned} E &= 6c^2-2c-1 \\\\ F &= -4c^2+7c+5 \end{aligned}
E, plus, F, equals, left parenthesis, 6, c, start superscript, 2, end superscript, minus, 2, c, minus, 1, right parenthesis, plus, left parenthesis, minus, 4, c, start superscript, 2, end superscript, plus, 7, c, plus, 5, right parenthesis
Rewrite without parentheses and color code like terms:
start color blueD, 6, c, start superscript, 2, end superscript, end color blueD, start color greenD, minus, 2, c, end color greenD, start color purpleD, minus, 1, end color purpleD, start color blueD, minus, 4, c, start superscript, 2, end superscript, end color blueD, start color greenD, plus, 7, c, end color greenD, start color purpleD, plus, 5, end color purpleD
Group like terms:
start color blue, left parenthesis, 6, minus, 4, right parenthesis, c, start superscript, 2, end superscript, end color blue, plus, start color green, left parenthesis, minus, 2, plus, 7, right parenthesis, c, end color green, plus, start color purple, left parenthesis, minus, 1, plus, 5, right parenthesis, end color purple
Simplify:
2, c, start superscript, 2, end superscript, plus, 5, c, plus, 4
Want to see another example? Check out this video.

Practice

Problem 1
Simplify.
left parenthesis, minus, 3, y, start superscript, 2, end superscript, minus, 5, y, minus, 2, right parenthesis, plus, left parenthesis, minus, 7, y, start superscript, 2, end superscript, plus, 5, y, plus, 2, right parenthesis

Want more practice? Check out these exercises: