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Adding and Subtracting Polynomials

When adding and subtracting polynomials , you can use the distributive property to add or subtract the coefficients of like terms.

Example 1:

Add.

( 2 x 2 + 5 x + 7 ) + ( 3 x 2 − 2 x + 5 )

Use the commutative property to group like terms.

= ( 2 x 2 + 3 x 2 ) + ( 5 x − 2 x ) + ( 7 + 5 )

Use the distributive property.

= ( 2 + 3 ) x 2 + ( 5 − 2 ) x + ( 7 + 5 ) = 5 x 2 + 3 x + 12

(Recall that "like terms" are monomials with the same variables, such as 3 x 2 y and 82 x 2 y .)

It may be helpful to arrange the like terms in columns, as with multi-digit addition.

Example 2:

Subtract.

( x 2 + 3 x y − 9 ) − ( − 2 y 2 + 5 x y + 6 )

Arrange vertically.

x 2 + 3 x y − 9 − − 2 y 2 + 5 x y + 6                                                                                                                   ¯

Subtract term by term.

x 2 + 3 x y − 9 − − 2 y 2 + 5 x y + 6       x 2 + 2 y 2 − 2 x y − 15 ¯ .

The solution is x 2 + 2 y 2 − 2 x y − 15 .