Combining Like Terms Notes

Combining Like Terms Notes

A variable is a symbol that represents an unspecified or unknown quantity. A variable is usually represented by a letter the alphabet. Examples: x, y, z, w, t, p, q

Like terms are terms that have the same variables in the same form or in equivalent forms so that the terms represent the same number. (x + x) (yz +zy)

·  The sign or the numerical coefficients do not matter when you are looking for like terms.

·  Sign + - or positive negative

·  Numerical Coefficients 234x 5pq 10w

To add, subtract, multiply, or divide like terms, you need to find terms that have the same exact variable(s) and perform the addition, subtraction, multiplication, or division to the coefficients.

·  4x + 6x = 10x 7y – 4z + 3y = 10y – 4z

When simplifying these expressions, you are combining like terms. You are not trying to solve to get an answer for the variables.

Examples:

1. Are these the same if x=4, y=3, z=2?

a.) xyz b.) yzx c.) xzy d.) yxz e.)zyx

4*3*2 = 24 3*2*4= 24 4*2*3=24 3*4*2= 24 2*3*4=24

Yes, they are the same because it does not matter what order you multiply in.

What are the variable(s) in each expression?

2. 6x 3. 7xy 4. 10p 5. r

x xy p r

What are the coefficients in each expression?

6. 5x 6. 8t 7. 128w 8. r

5 8 128 1

(if no number, assume 1)

Simplify:

9. 6x + 3x 10. 5z + -3 + -2z

9x 3z + -3

11. -5w + 6zw + -3w + 8 12. 7p + p + p

-8w + 6zw + 8 9p

13. t + 6t + -4t 14. 16q + 4 + -8q

3t 8q + 4

15. 7xy + 8yx 16. 3ptw + -4pt + 3tp

15xy OR 15yx 3ptw + -pt OR 3ptw + -tp

Name: Core #:

Classwork on adding Like Terms

1. Are these the same if w=3, p=2, r=5?

a.) wpr b.) prw c.) rwp d.) pwr e.) wrp

What are the variable(s) in each expression?

2. 23p 3. 12tw 4. 7yz 5. q

What are the coefficients in each expression?

6. 89x 6. 126t 7. 19w 8. r

Simplify:

9. 7x + 5x 10. 14w + -6 +-3w

11. -9p +6zw + -6w + 4 12. 4p + p + p

13. r + 3r + -2r 14. 24t + -3 + -8t

15. 14zy + 5yz + -6z + 4y 16. 2xy + 3xz + -yz + 4x