I'm stuck on how to completely factor y^3 + x + x^3 + y
This is what I have so far:
Since addition is associative we can rearrange the terms so y^3 and x^3 are next to each other
= y^3 + x^3 + x + y
We see more clearly that y^3 + x^3 forms a sum of two cubes and we can apply the formula: A^3 + B^3 = (A + B) (A^2 - AB + B^2)
= (y + x) (y^2 - xy + x^2) + x + y
This is where I'm stuck, I don't know what to do with the "extra" x + y.
I looked up the solution in the back of the book and it's (y + x)(y^2 -xy +x^2 +1), which is pretty close to what I have so far, so I know I'm on the right track.
This is what I have so far:
Since addition is associative we can rearrange the terms so y^3 and x^3 are next to each other
= y^3 + x^3 + x + y
We see more clearly that y^3 + x^3 forms a sum of two cubes and we can apply the formula: A^3 + B^3 = (A + B) (A^2 - AB + B^2)
= (y + x) (y^2 - xy + x^2) + x + y
This is where I'm stuck, I don't know what to do with the "extra" x + y.
I looked up the solution in the back of the book and it's (y + x)(y^2 -xy +x^2 +1), which is pretty close to what I have so far, so I know I'm on the right track.
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