Example

Adding (5y23y+15)+(3y24y11)(5y^2 - 3y + 15) + (3y^2 - 4y - 11)

Find the sum of two trinomials:

(5y23y+15)+(3y24y11)(5y^2 - 3y + 15) + (3y^2 - 4y - 11)

Step 1 — Identify like terms: The y2y^2-terms are 5y25y^2 and 3y23y^2; the yy-terms are 3y-3y and 4y-4y; the constants are 1515 and 11-11.

Step 2 — Rearrange to group like terms together: Using the Commutative Property of Addition, reorder so that matching terms are adjacent:

5y2+3y23y4y+15115y^2 + 3y^2 - 3y - 4y + 15 - 11

Step 3 — Combine like terms: Add the coefficients within each group: 5+3=85 + 3 = 8 gives 8y28y^2; 3+(4)=7-3 + (-4) = -7 gives 7y-7y; 15+(11)=415 + (-11) = 4.

The sum is 8y27y+48y^2 - 7y + 4.

This example demonstrates that adding two polynomials requires no special rules beyond identifying and combining like terms — the same three-step process used for simpler expressions applies directly when entire polynomials are added together.

Image 0

0

1

Updated 2026-04-21

Contributors are:

Who are from:

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.6 Polynomials - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Related
Learn After