COMBINING LIKE TERMSSection 1.4

TERMSTerms are separated by + and –

signs in an algebraic expression

(3 terms)

LIKE TERMS UNLIKE TERMS

4 𝑥+8𝑥 3 𝑥+5

2 𝑦−7 𝑦 3 𝑥−7 𝑦

5 𝑥2+7 𝑥2 2 𝑥2+6 𝑥

−2 𝑥𝑦2−9 𝑥 𝑦 2 9 𝑥𝑦2+2 𝑥2

LIKE TERMSTerms that contain the same

variables, with corresponding variables having the same power.

HANDS-ON EQUATIONSBlue Pawn: Positive xWhite Pawn: Negative xGreen Cube: Positive numbers

Red Cube: Negative numbers

REPRESENT

3x+5+2x+2

REPRESENT

2x+3+5x-6

REPRESENT

-3x+1-2x-6

REPRESENT

4x-8-5x+2

SIMPLEST FORM Contains no like terms and no parentheses.

COMBINING LIKE TERMS

Application of the distributive property.

COEFFICIENT

It is the numerical factor. The number being multiplied by the variable.

To combine like terms we can simply combine the coefficients of the like terms.

SIMPLIFY:

17 𝑥+18 𝑦+3 𝑥+5

SIMPLIFY:

6 𝑥2+7 𝑥−2 𝑥2−4 𝑥

SIMPLIFY:

8 𝑦3−7 𝑦+6 𝑦 2+3 𝑦3−4 𝑦

SIMPLIFY:

2 𝑥−3 𝑦+8 𝑥−7 𝑦+3

SIMPLIFY:

7 𝑦2−10 𝑦−12 𝑦+4 𝑥2

SIMPLIFY:

5 (3 𝑥+7 )−8 𝑥

SIMPLIFY:

6 (2 𝑥−3 )−8 (5𝑥−2)

SIMPLIFY:

−4 (7 𝑥−8 )−(3 𝑥+9)

SIMPLIFY:

5 (2 𝑥+3 𝑦 )+4 (𝑥−2 𝑦 )+3

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