Question

250x^3-128y^3
factor

Answer 1

We can use the difference of cubes formula: \(a^3-b^3=(a-b)(a^2+ab+b^2)\). Here \(a = 125^{1/3}x\) and \(b = 64^{1/3}y\):

$$
250x^3-128y^3\\
=2(125x^3-64y^3)\\
\text{Applying formula above:}\\
=2(125^{1/3}x-64^{1/3}y)(125^{2/3}x^2+125^{1/3}x64^{1/3}y+64^{2/3}y^2)\\
=2(5x-4y)(5^2x^2+5x4y+4^2y^2)\\
=2(5x-4y)(25x^2+20xy+16y^2)\\
$$

That's it!

Let me know if you have any questions.