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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

\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}{u}^{2}v+5{u}^{2}-3{v}^{2}\hfill \\ \text{There are no like terms to combine.}\hfill & & & \phantom{\rule{4em}{0ex}}{u}^{2}v+5{u}^{2}-3{v}^{2}\hfill \end{array}\)

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