Adding and Subtracting Polynomials

Adding and Subtracting Polynomials

How to add and subtract the terms in a polynomial: examples and their solutions.

Example 1

Simplify the given expression. 7x^2 - 3x + 2x^2 + 8x

Only like terms
(terms that have the same variables & exponents)
can be added or subtracted.

7x2 and +2x2 are like terms.
So 7x2 + 2x2 = (7 + 2)x2.

-3x and +8x are like terms.
So -3x + 8x = (-3 + 8)x.

Example 2

Simplify the given expression. 3a^2 + 2ab + ab^2 - 6ab + 9ab^2 - a^2

3a2 and -a2 are like terms. (blue)
So 3a2 - a2 = (3 - 1)a2.

+ab2 and +9ab2 are like terms. (green)
So ab2 + 9ab2 = (1 + 9)ab2.

+2ab and -6ab are like terms. (red)
So +2ab - 6ab = (2 - 6)ab.