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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