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Math Help - Factoring help

  1. #1
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    Factoring help

    How do you factor
    (a+b)^2-(2a-b)^2
    and
    (a+b)^2-4(b+c)^2
    without simplifying the expression?
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  2. #2
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    Quote Originally Posted by sinjid9 View Post
    How do you factor
    (a+b)^2-(2a-b)^2
    and
    (a+b)^2-4(b+c)^2
    without simplifying the expression?
    Each of them is a difference of two squares.

    Remember that (x + y)(x - y) = x^2 - y^2.



    (a + b)^2 - (2a - b)^2 = [(a + b) + (2a - b)][(a + b) - (2a - b)]

     = 3a(2b - a).



    (a+b)^2-4(b+c)^2 = (a + b)^2 - [2(b + c)]^2

     = (a + b)^2 - (2b + 2c)^2

     = [(a + b) + (2b + 2c)][(a + b) - (2b + 2c)]

     = (a + 3b + 2c)(a - b - 2c).
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sinjid9 View Post
    How do you factor
    (a+b)^2-(2a-b)^2
    and
    (a+b)^2-4(b+c)^2
    without simplifying the expression?
    (a+b)^2-(2a-b)^2 is in the form of x^2-y^2 where x = a+b and y = (2a-b)

    you should know that a^2-b^2=(a-b)(a+b)
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  4. #4
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    Thanks for the help, both of you.
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