How do you factor #c^3 - 512#?

1 Answer
Bhavin B.
May 2, 2018

#(c-8)(c^2+8c+64)#

Explanation:

Rewrite #512=8^3#
Then we get #C^3 - 8^3#
Now we can use the perfect square formula:
#a^3 - b^3# = #(a - b)(a^2+ab+b^2)# where #a=c# and #b=8#

#c^3 - 8^3# = #(c-8)(c^2+c.8+8^2)#

#c^3 - 8^3# = #(c-8)(c^2+8c+64)#

Since #(c^2+8c+64)# cannot be factorized any more, the answer remains the same:

#c^3 - 8^3# = #(c-8)(c^2+8c+64)#

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