Example

Adding (5y2−3y+15)+(3y2−4y−11)(5y^2 - 3y + 15) + (3y^2 - 4y - 11)

Find the sum of two trinomials:

(5y2−3y+15)+(3y2−4y−11)(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+3y2−3y−4y+15−115y^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 8y2−7y+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.

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Updated 2026-04-21

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