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Factor each of the following by using the distributive property. (a) 14x +21 (b) 6-3x

User Zaneta
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You have the following two expressions:

a) 14x + 21

b) 6 - 3x

In order to find the factor for each expression, you consider that the factor is a term which multiplied by the terms inside the parenthesis generates the original expression. The factor is deduced from the estimation of the least common multiple of the terms.

a) 14x + 21

you have that least common multiple is 7. Then, you have:

14x + 21 = 7(2x + 3)

next, you use the distribution property in the expression 7(2x + 3)

7(2x + 3) = (7)(2x) + (7)(3) = 14x + 21

thus, you obtain the original expression and 7 is in fact, the searched factor.

b) 6 - 3x

the least common multiple of this expression is 3. Then, you have:

6 - 3x = 3(2 - x)

next, you use distribution property

3( 2 - x ) = (3)(2) + (3)(-x) = 6 - 3x

thus, the factor is 3

User Nnachefski
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