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Math Help - [SOLVED] Difference of two Squares

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    [SOLVED] Difference of two Squares

    Q.Use the difference of two squares method to factorise:

    (y + 4)^2 - (y - 2)^2

    the answer is 12(y + 1) but i have absolutely no idea how to work it out.

    thanks
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    Quote Originally Posted by waven View Post
    Q.Use the difference of two squares method to factorise:

    (y + 4)^2 - (y - 2)^2

    the answer is 12(y + 1) but i have absolutely no idea how to work it out.
    Do you know how to factor a difference of squares? Use

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

    Compare this with what you have. Then you should see that a=y+4 and b=y-2. Go ahead and substitute, and then simplify.
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  3. #3
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    Quote Originally Posted by Reckoner View Post
    Do you know how to factor a difference of squares? Use

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

    Compare this with what you have. Then you should see that a=y+4 and b=y-2. Go ahead and substitute, and then simplify.
    ok i got
    =(y+4+y-2)(y+4-y-2)
    =(2y+2)(2)
    =2y+4
    =2(y+2)
    thats definately wrong, could someone perhaps show me the full working please from beginning to end?
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  4. #4
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    Quote Originally Posted by waven View Post
    ok i got
    =(y+4+y-2)(y+4-y-2)
    =2y+2+2
    =2y+4
    =2(y+2)
    thats definately wrong, could someone perhaps show me the full working please from beginning to end?
    You have said that y+4-(y-2) = y+4 - y - 2 which is incorrect. (y+4)-(y-2) = y+4-y+2 = 6 since subtracting a negative means you add it on.

    Doing that gives you 6(2y+2) = 12y+12 = 12(y+1)

    ----------

    [(y+4)+(y-2)] \times [(y+4)-(y-2)]
    (y+4+y-2) \times (y+4-y+2)
    (2y+2) \times 6
    6(2y+2) = 6 \times 2(y+1) = 12(y+1)
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