How do you factor 5c^2-24cd-5d^2?

1 Answer
George C.
May 9, 2016

5c^2-24cd-5d^2 = (c-5d)(5c+d)

Explanation:

Here's one way...

Multiply through by 5, complete the square, use the difference of squares identity:

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

with a=(5c-12d) and b=13d, then divide by 5...

5(5c^2-24cd-5d^2)

=25c^2-120cd-25d^2

=(5c-12d)^2-(12d)^2-25d^2

=(5c-12d)^2-(144+25)d^2

=(5c-12d)^2-169d^2

=(5c-12d)^2-(13d)^2

=((5c-12d)-13d)((5c-12d)+13d)

=(5c-25d)(5c+d)

=5(c-5d)(5c+d)

So:

5c^2-24cd-5d^2 = (c-5d)(5c+d)

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