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Question 636668: Show all work. Find the quotient: (16a^2 -b^2)/(4a -b)
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! The term 16a^2 can be expessed as 4^2*a^2. Using the property that the product of two squares is equal to the square of the products, 16a^2 can be expressed as (4a)^2. Then the numerator is the difference of two perfect squares (4a)^2 and b^2, therefore can be factored into the product of the sum and difference of the numbers being squared. In this case we have
{(4a)^2 - b^2} = (4a + b)(4a - b)
You can check this factorization by "FOIL",
(4a)*(4a) -4ab +4ab - b*b = (4a)^2 - b^2 = 16a^2 - b^2
Note that the "OI" terms of "FOIL" cancel. This does not happen when the two perfect squares are added.
Rewriting the given expression yields
{(4a + b)(4a - b)}/(4a - b)
which simplifies to the quotient
4a + b
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