How do you factor c^3 - 512c3−512?

1 Answer
Bhavin B.
May 2, 2018

(c-8)(c^2+8c+64)(c−8)(c2+8c+64)

Explanation:

Rewrite 512=8^3512=83
Then we get C^3 - 8^3C3−83
Now we can use the perfect square formula:
a^3 - b^3a3−b3 = (a - b)(a^2+ab+b^2)(a−b)(a2+ab+b2) where a=ca=c and b=8b=8

c^3 - 8^3c3−83 = (c-8)(c^2+c.8+8^2)(c−8)(c2+c.8+82)

c^3 - 8^3c3−83 = (c-8)(c^2+8c+64)(c−8)(c2+8c+64)

Since (c^2+8c+64)(c2+8c+64) cannot be factorized any more, the answer remains the same:

c^3 - 8^3c3−83 = (c-8)(c^2+8c+64)(c−8)(c2+8c+64)

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