+66 Completely factor 27x3 - 512y3
AND
Completely factor 4x2-9y2
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.
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!
