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Math Help - Factorization

  1. #1
    Junior Member
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    Factorization

    Factorize:
    25- p^2 - q^2 - 2pq is
    (a)(5+p+q)(5-p+q)
    (b)(5+p+q)(5-p-q)
    (c)(5+p+q)(5+p-q)
    (d)(5+p-q)(5-p+q)
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  2. #2
    Member
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    Hello,

    Hints: (p+q)^2=? (p-q)^2=? (p+q)(p-q)=?

    Warnig: Don' t forget the parentheses for grouping!

    Bye.
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  3. #3
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    Hello, devi!

    Factorize: . 25- p^2 - q^2 - 2pq

    . . \begin{array}{cc}(a)\;(5+p+q)(5-p+q) & (b)\;(5+p+q)(5-p-q) \\ \\[-3mm] (c)\;(5+p+q)(5+p-q) & (d)\;(5+p-q)(5-p+q)\end{array}

    We have: . 25 - (p^2 + 2pq + q^2) \;=\;25 - (p + q)^2\quad\hdots a difference of squares!

    . . . =\;\bigg[5 + (p+q)\bigg]\,\bigg[5 - (p+q)\bigg] \;=\;(5 + p + q)(5 - p - q)\;\;{\color{blue}(b)}

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