## Rebbbtx 3 years ago Can someone please show me step by step, how to factor this equation? a^3x-b^3x-a^3y+b^3y the answer = (a-b)(a^2+ab+b^2)(x-y)

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1. sauravshakya

a^3x-b^3x-a^3y+b^3y (a^3-b^3)x - (a^3 -b^3)y

2. sauravshakya

Did u get that step?

3. Rebbbtx

okay, yes. First you take the x and y out

4. Rebbbtx

what next?

5. Hezekieli

One could also start by taking a and b out:\[a^{3}(x-y)+b^{3}(y-x)\] But I don't really know how to get to that answer or why to aim at that? :o

6. andriod09

The best way to do it: FIND THE COMMON NUMBER BETWEEN EVERYTHING.

7. abdul_shabeer

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

8. abdul_shabeer

9. Hezekieli

You can check that what abdul said by going backwards: \[(a - b)(a ^{2} + ab + b ^{2})\] \[= (a^{3}+a^{2}b + ab^{2}) + (-a^{2}b - ab^{2} - b^{3})\] \[= a^{3}+a^{2}b - a^{2}b + ab^{2} - ab^{2} - b^{3}\] \[= a^{3} - b^{3}\] Not sure yet how to get that (x - y) out o.O

10. abdul_shabeer

\[a^3x-b^3x-a^3y+b^3y\] \[x(a^3-b^3)-y(a^3-b^3)\] \[(a^3-b^3)(x-y)\] \[(a-b)(a^2+ab+b^2)(x-y)\]