Adding and Subtracting Polynomials

Add and Subtract Monomials

You have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficient.

Example 6.3

Add: \(25 y^{2}+15 y^{2}\).

Solution

	\(25 y^{2}+15 y^{2}\)
Combine like terms.	\(40 y^{2}\)

Try It 6.5

Add: \(12 q^{2}+9 q^{2}\).

Try It 6.6

Add: \(-15 c^{2}+8 c^{2}\).

Example 6.4

Subtract: \(16p−(−7p)\).

Solution

	\(16p−(−7p\))
Combine like terms.	\(23p\)

Try It 6.7

Subtract: \(8 m-(-5 m)\).

Try It 6.8

Subtract: \(-15 z^{3}-\left(-5 z^{3}\right)\).

Remember that like terms must have the same variables with the same exponents.

Example 6.5

Simplify: \(c^{2}+7 d^{2}-6 c^{2}\).

Solution

	\(c^{2}+7 d^{2}-6 c^{2}\)
Combine like terms.	\(-5 c^{2}+7 d^{2}\)

Try It 6.9

Add: \(8 y^{2}+3 z^{2}-3 y^{2}\).

Try It 6.10

Add: \(3 m^{2}+n^{2}-7 m^{2}\).

Example 6.6

Simplify: \(u^2v+5u^2−3v^2\).

Solution

	\(u^{2} v+5 u^{2}-3 v^{2}\)
There are no like terms to combine.	\(u^{2} v+5 u^{2}-3 v^{2}\)

Try It 6.11

Simplify: \(m^{2} n^{2}-8 m^{2}+4 n^{2}\).

Try It 6.12

Simplify: \(p q^{2}-6 p-5 q^{2}\).