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Completely factor 27x- 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. 

 Jan 30, 2020
 #1
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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! 

 Jan 31, 2020

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