Recall that a term is a number, a variable, or a product or quotient of numbers and variables.   Like terms are terms that contain the same variable, with corresponding variables having the same power.

3x²+2x–5 has 3 distinct terms, no like terms

2y²+6y²+5y has 3 terms and 2 of them are like terms.   We can simplify this expression by combining the like terms, 2y² and 6y² to get 8y²+5y.

Example:

The distributive property and the properties of equality can be used to show that

An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.

Practice

Evaluate each expression for the given value of the variable.
1. 8m – 5 for m = 9
2. 3n + 4 for n = 3
3. y ÷ 7 for y = 49
4. k x 4 – 6 for k = 3

Write each phrase as a numerical or algebraic expression.
5. 26 more than n
6. the product of 6 and 5

Simplify each expression.
7. 5 + 3x + 2y + x – 7 + 4y
8. 3x² + 18 – 3x + 3x² + 9x + 5x
9. -2x + x² – x + 4x² + 6x² + 8x + 1
10. 2x + 4x + 7 + 4
11. 4x – 10 – x – 1
12. 9x + 9x – 2 – 6 – 9x
13. 7xy – 3xy + 4
14. 7x + 2y + 5x + 9y + 3x

 

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