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Thread: binomial

  1. #1
    Junior Member
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    binomial

    I need to factor this completely:

    $\displaystyle 16x^2 - (y + 3)^2$

    $\displaystyle
    16x^2 - (y + 3)^2
    = [16x - (y+3)]^2
    = [4x - (y+3)]^2
    = (2x - y - 3)(2x + y + 3)$

    but the answer in the packet says:

    $\displaystyle (4x + y + 3)(4x - y - 3)$

    My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?
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  2. #2
    MHF Contributor
    Joined
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    Quote Originally Posted by lax600 View Post
    I need to factor this completely:

    $\displaystyle 16x^2 - (y + 3)^2$

    $\displaystyle
    16x^2 - (y + 3)^2
    = [16x - (y+3)]^2
    = [4x - (y+3)]^2
    = (2x - y - 3)(2x + y + 3)$

    but the answer in the packet says:

    $\displaystyle (4x + y + 3)(4x - y - 3)$

    My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?
    You're just not correctly converting the difference of squares. We have:

    $\displaystyle 16x^2 = a^2$

    $\displaystyle (y+3)^2 = b^2$

    Hence, $\displaystyle a = 4x$ and $\displaystyle b = y + 3$.

    So, using the formula $\displaystyle a^2 - b^2 = (a + b)(a - b)$ we have:

    $\displaystyle (4x + y + 3)(4x - y - 3)$.
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  3. #3
    Junior Member
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    Mar 2008
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    Oh! Alright thanks ^^
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