How do you factor c^ { 3} + 64c3+64?

2 Answers
Dec 17, 2016

(c + 4)xx(c^2- 4c + 16)(c+4)×(c24c+16)

Explanation:

There is a Theory:

A sum of two perfect cubes, a^3+b^3a3+b3 can be factored into
(a+b)xx(a^2-ab+b^2)(a+b)×(a2ab+b2)

So c^3+64=c^3+4^3c3+64=c3+43
(c+4)xx(c^2-4c+4^2)(c+4)×(c24c+42)
(c+4)xx(c^2-4c+16)(c+4)×(c24c+16)

Dec 17, 2016

(c^3+64) = (c+4)(c^2-4c+16)(c3+64)=(c+4)(c24c+16)

Explanation:

The generalized factoring of x^3+a^3x3+a3 is (x+a)(x^2-ax+a^2)(x+a)(x2ax+a2)
as demonstrated below:

{: (xx," | ",x^2,-ax,a^2), ("-----",,"-----","-----","-----"), (x," | ",x^3,-ax^2,a^2x), (a," | ",ax^2,-a^2x,a^3), ("-----","-----","-----","-----","-----"), (,x^3,,,a^3) :}