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Adding and Subtracting Polynomials

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Adding and Subtracting 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: \(\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x-9\right).\)

Solution

 Adding and Subtracting Polynomials
Identify like terms.Adding and Subtracting Polynomials
Rearrange to get the like terms together.Adding and Subtracting Polynomials
Combine like terms.Adding and Subtracting Polynomials

Parentheses are grouping symbols. When we add polynomials as we did in the previous lesson, 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.

Optional Video: Adding Polynomials

Example

Find the difference: \(\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right).\)

Solution

 Adding and Subtracting Polynomials
Distribute and identify like terms.Adding and Subtracting Polynomials
Rearrange the terms.Adding and Subtracting Polynomials
Combine like terms.Adding and Subtracting Polynomials

Example

Subtract: \(\left({m}^{2}-3m+8\right)\) from \(\left(9{m}^{2}-7m+4\right).\)

Solution

 Adding and Subtracting Polynomials
Distribute and identify like terms.Adding and Subtracting Polynomials
Rearrange the terms.Adding and Subtracting Polynomials
Combine like terms.Adding and Subtracting Polynomials

Optional Video: Subtracting Polynomials

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