Question

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

Answer 1

`(c + 4)xx(c^2- 4c + 16)`

Explanation:

There is a Theory:

A sum of two perfect cubes, `a^3+b^3` can be factored into
`(a+b)xx(a^2-ab+b^2)`

So `c^3+64=c^3+4^3`
`(c+4)xx(c^2-4c+4^2)`
`(c+4)xx(c^2-4c+16)`

Answer 2

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

Explanation:

The generalized factoring of `x^3+a^3` is `(x+a)(x^2-ax+a^2)`
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) :}#