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The distributive property
Definitions
Distributive property : for any number a, b,
and c, then:
a(b+c) = ab + ac and (b+c)a = ba + ca
a(b-c) = ab – ac and (b-c)a = ba – ca
Example: 6( x + 4) = 6x + 24
Formula for the area of a triangle:
A=L*W
where A = area, L = length and W = width
Definitions cont.
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Term: is a number, a variable, or a product or
quotient of numbers and variables.
Example: 5, x, 3y, b/9
Simplest form: combine like terms and has
no parenthesis.
Example: 3x + x + 4y – 2y = 4x + 2y
Coefficient: The coefficient of a term is the
numerical factor.
Example: for 14xy, 14 is the coefficient.
Practice
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Use the distributive property to rewrite each
expression without parenthesis:
1.) a(5 – b)
= 5a – ab
2.) 4(y + 2)
= 4y + 8
3.) 6(5x + 3)
= 30x + 18
Practice
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Simplify each expression, if possible. If
not possible, write in simplest form.
1.) 5a + 7a + 10b + 5b
Answer: 12a + 15b
2.) 7( 3x^2y – 4xy^2 + xy)
Answer: 21x^2y –28xy^2 + 7xy