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Bellwork Simplify 1.) (2 + 3x) + 9 2.) 9(2x)
3.) Name the property for: 3 x 0 = 0
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1-7 The Distributive Property
By Kari Vang
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Term & Like terms A term is a number, a variable or a product or quotient of numbers and variables. For example, 5, x, or 4y, or ½r Like terms are terms that contain the same variables, with corresponding variables having the same power. For example, a + 2a
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Coefficient The coefficient of a term is the numerical factor .
In other words, the coefficient is always the number in front of the variable whether shown or assumed. For example, in 4y, the coefficient is 4. Reminder to discuss zero as a coefficient. 0x = 0 1xy = xy They need to be able to name coefficients of given examples, esp. with fractions.
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Coefficient (cont’d) In xy, the coefficient is an assumed 1. 1xy = xy
One is always the assumed coefficient if it is not shown.
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Adding Like Terms When adding like terms, add the coefficients together and rewrite the variable/s along with the same exponent. For example, 5c – 2c 12x + x y – 2y
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Simplify each expression by adding like terms. Ex. 1
a.) 6y + 2y c.) 4ab + 3a + 7ab b.) 4x – 3 – 5x d.) 5x² + 2x – 3x²
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Distributive Property
For any numbers a,b, and c, a(b + c) = ab + ac and (b + c)a = ba + ca; a(b – c) = ab – ac and (b – c)a = ba – ca.
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Use the Distributive Property to rewrite each expression. Ex. 2
a.) 2(a + 3) c.) -(x + 5) b.) -(b – 5) Use Product Map and Algebra Tiles
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Use the Distributive Property to find each product. Ex. 3
Simplify each expression by combining like terms a.) 4x + 12x c.) 3d – 4 + 5d + 1 b.) 9y – y d.)
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