Completely factor 27x^{3 }- 512y^{3}

AND

Completely factor 4x^{2}-9y^{2}

I am having issues with these certain problems. Please explain if possible how to do this. I want to figure it out but it's not on any of my lessons that the teacher has released.

KaylaDoodlez Jan 30, 2020

#1**+2 **

Hello KaylaDoodlez,

For the first one:

\(27x^3-512y^3\)

If you want "Binomial factoring"

Then there is no common factor for 27 and 512

Thus factoring it by a common factor isn't possible.

There is a formula for this:

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

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

We will use the second one as it is similar to your question "Difference between the two cubics"

\((3x-8y)(9x^2-24xy+64y^2)\)

Second question:

Difference between squares.

\(a^2-b^2=(a+b)(a-b)\)

\(4x^2-9y^2=(2x-3y)(2x+3y)\)

hope that helped, you really need to memorize the formula and have practice!

Guest Jan 31, 2020