Adding and Subtracting Monomials
Adding and Subtracting 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
Add: \(25{y}^{2}+15{y}^{2}\).
Solution
\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}25{y}^{2}+15{y}^{2}\hfill \\ \text{Combine like terms.}\hfill & & & \phantom{\rule{4em}{0ex}}40{y}^{2}\hfill \end{array}\)
Example
Subtract: \(16p-\left(-7p\right)\).
Solution
\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}16p-\left(-7p\right)\hfill \\ \text{Combine like terms.}\hfill & & & \phantom{\rule{4em}{0ex}}23p\hfill \end{array}\)
Remember that like terms must have the same variables with the same exponents.
Example
Simplify: \({c}^{2}+7{d}^{2}-6{c}^{2}\).
Solution
\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}{c}^{2}+7{d}^{2}-6{c}^{2}\hfill \\ \text{Combine like terms.}\hfill & & & \phantom{\rule{4em}{0ex}}-5{c}^{2}+7{d}^{2}\hfill \end{array}\)
Example
Simplify: \({u}^{2}v+5{u}^{2}-3{v}^{2}\).
Solution
\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}{u}^{2}v+5{u}^{2}-3{v}^{2}\hfill \\ \text{There are no like terms to combine.}\hfill & & & \phantom{\rule{4em}{0ex}}{u}^{2}v+5{u}^{2}-3{v}^{2}\hfill \end{array}\)
This lesson is part of:
Polynomials II