Learning Outcomes
- Add polynomials
- Subtract polynomials
In a previous lesson, you learned how to simplify expressions by combining like terms. Adding and subtracting monomials is the same as combining like terms. Like terms must have the same variable with the same exponent. Recall that when combining like terms only the coefficients are combined, never the exponents.
example
Add: [latex]17{x}^{2}+6{x}^{2}[/latex]
Solution
| [latex]17{x}^{2}+6{x}^{2}[/latex] | |
| Combine like terms. | [latex]23{x}^{2}[/latex] |
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example
Subtract: [latex]11n-\left(-8n\right)[/latex]
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example
Simplify: [latex]{a}^{2}+4{b}^{2}-7{a}^{2}[/latex]
try it
Watch the following video for more examples of how to multiply polynomials.
Add and Subtract Polynomials
Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms—those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.
Example
Find the sum: [latex]\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right)[/latex].
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Parentheses are grouping symbols. When we add polynomials as we did in the last example, we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.
example
Find the difference: [latex]\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right)[/latex].
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Exercises
Subtract [latex]\left({m}^{2}-3m+8\right)[/latex] from [latex]\left(9{m}^{2}-7m+4\right)[/latex].
TRY IT
In the next video we show more examples of adding and subtracting polynomials.
