Mathematics » Introducing Polynomials » 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

 Identify like terms. Rearrange to get the like terms together. Combine like terms.

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.

## Example

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

### Solution

 Distribute and identify like terms. Rearrange the terms. Combine like terms.

## Example

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

### Solution

 Distribute and identify like terms. Rearrange the terms. Combine like terms.

### Optional Video: Subtracting Polynomials

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