Question

Identify whether the problem is "Sum of Two Cubes" or "Difference of Cubes". Then, factor the problem. 8.) x^3 + 125

Answer 1

We can answer this question if we have into account that:

$a^3+b^3=(a+b)\cdot(a^2-ab+b^2)$

And

$a^3-b^3=(a-b)\cdot(a^2+ab+b^2)$

These are the cases for perfect cubes. Since we have that:

$x^3_{}+125=x^3+5^3$

Then, we have:

a = x

b = 5

$(x+5)\cdot(x^2-5x+5^2)=(x+5)\cdot(x^2-5x+25)$

Then, the factored form of the perfect cubes is:

$(x+5)\cdot(x^2-5x+25)$