SOLUTION: Factor (2x+y)^2-49

Question 764618: Factor (2x+y)^2-49
Found 2 solutions by DrBeeee, MathLover1:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given:
(1) (2x+y)^2-49
This expression is the difference of two perfect squares which factors into the the product of the sum and difference of their square roots. For example
(2) (a^2-b^2) = (a+b)*(a-b)
In your case
(3) a^2 = (2x+y)^2 or
(4) a = 2x+y and
(5) b^2 = 49 or
(6) b = 7
Then the given expression of (1) factors into
(7) (2x+y+7)*(2x+y-7}
Let's FOIL (7) to see if we get (1).
(8) (2x+y+7)*(2x+y-7} = (2x+y)*(2x+y)-7*(2x+y)+7*(2x+y)+7*(-7} or
(9) (2x+y+7)*(2x+y-7} = (2x+y)^2 -7*(2x+y)+7*(2x+y) -49 or
(10) (2x+y+7)*(2x+y-7} = (2x+y)^2 -49 which is the same as (1)
Answer: (2x+y)^2-49 = (2x+y+7)*(2x+y-7}

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

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