1.2 Distributive Property & Combining Like Terms

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Presentation transcript:

1.2 Distributive Property & Combining Like Terms How can “Combining Like Terms” and the “Distributive Property” be used to simplify expressions?

8 Constant 7 x 2 Exponent Like terms: Rules: Same Variable and same exponent Coefficients can be different 3. Constants are like terms (ie. like 5 and 3 ) Like Terms Unlike Terms -3x and 2x 5x2 and 2x The exponents are different. 3.2 and n Only one term contains a variable 6a and 6b The variables are different w and w 7 5 and 1.8 7 x Coefficient Variable 8 Constant 2 Exponent

Identify like terms in the list. 3t 5w2 7t 9v 4w2 8v Look for like variables with like powers. 3t 5w2 7t 9v 4w2 8v Like terms: (3t and 7t) (5w2 and 4w2) (9v and 8v)

Simplify. A. 6t – 4t 6t – 4t 6t and 4t are like terms. 2t Subtract the coefficients. B. 45x – 37 – x + 4

Write an expression using the side lengths. 2x + 3 + 3x + 2 + x Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. x 2x + 3 3x + 2 Write an expression using the side lengths. 2x + 3 + 3x + 2 + x (x + 3x + 2x) + (2 + 3) Identify and group like terms. 6x + 5 Add the coefficients.

Your Turn: -5a + 4 - 2a -x + 2 + 8x - 5 6x + 8y 2x + 3 x + 1 3. Write an expression for the perimeter of the given figure 2x + 3 x + 1

You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

Simplify the expressions: –2(3 – d)

Simplify the expression: 3d – (9 – 2d)