Combining Like Terms

Objective

Know how to simplify an expression by combining like terms

Example

Simplify

3+5z²-4y-4y²-3z-7+10y-10z+9y²+7z²

Answer: 5y²+12z²+6y-13z-4

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Explanation

Like much of math, the purpose of combining like terms is to make our answers look nicer, and make them easier to do math with. Look at the example above and you'll see how much nicer the answer looks.

So, which terms can be combined?

• all numbers without variables can be combined.

• all terms that have the same variable raised to the same power can be combined.

Lets take another look at our introductory example

3+5z²-4y-4y²-3z-7+10y-10z+9y²+7z²

-4y²+9y² = 5y²

+5z²+7z² = 12z²

-4y+10y = 6y

-3z-10z = -13z

3-7 = -4

Putting these together: 5y²+12z²+6y-13z-4

Answer: 5y²+12z²+6y-13z-4

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Examples

Example 1

Simplify

3z^2+6z^2+6 or 3z²+6z²+6 when typing on a computer

3z²+6z²+6

Answer: 9z²+6 or 9z^2+6 when typing on a computer

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Example 2

7+9z^2-3y-3z-3+9y-3z+3y^2

7+9z^2-3y-3z-3+9y-3z+3y^2

+3y^2

+9z^2

-3y+9y = 6y

-3z-3z = -6z

7-3 = 4

Answer: 3y^2+9z^2+6y-6z+4

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Practice your skills