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Math Help - Not sure what this is called.

  1. #1
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    Not sure what this is called.

    I am not sure what this type of equation is called, but anyway this is the formula

    (3x+2y)^2 – (x-y)^2
    4x + 6y

    And the answer is =2x + y/2

    So i know i have to factor out the numerator but for the life of me i cannot see how they come up with that answer, can anyone please explain how this works?

    Much appreciated.


    p.s what this type of equation called?
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  2. #2
    Super Member
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    Quote Originally Posted by Lucy1 View Post
    I am not sure what this type of equation is called, but anyway this is the formula

    (3x+2y)^2 – (x-y)^2
    4x + 6y

    And the answer is =2x + y/2

    So i know i have to factor out the numerator but for the life of me i cannot see how they come up with that answer, can anyone please explain how this works?

    Much appreciated.


    p.s what this type of equation called?
    I'd call this a rational expression.

    The numerator is a difference of two squares:
    a^2 - b^2 = (a + b)(a - b)

    In our case, a = 3x + 2y and b = x - y, so
    \frac{(3x + 2y)^2 - (x - y)^2}{4x + 6y}
    \begin{aligned}<br />
&= \frac{[(3x + 2y) + (x - y)][(3x + 2y) - (x - y)]}{2(2x + 3y)} \\<br />
&= \frac{(4x + y)(2x + 3y)}{2(2x + 3y)} \\<br />
&= \frac{4x + y}{2} \\<br />
&= \frac{4x}{2} + \frac{y}{2} \\<br />
&= 2x + \frac{y}{2} \\<br />
\end{aligned}


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  3. #3
    MHF Contributor red_dog's Avatar
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    Use the formula a^2-b^2=(a-b)(a+b)

    (3x+2y)^2-(x-y)^2=[(3x+2y)-(x-y)][(3x+2y)+(x-y)]

    Can you continue?
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  4. #4
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    yip i understand that , thanks alot, now i can attempt some other examples.

    Thanks!!
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