What is factor (x*y)^3-27-y^3+27x^3 ?

The solution to factor (x*y)^3-27-y^3+27x^3 is (x^2+1+x)(-1+x)(y+3)(y^2-3y+9)

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factor (x*y)^3-27-y^3+27x^3

factor

(x \cdot y)^{3} - 27 - y^{3} + 27 x^{3}

(x^{2} + 1 + x) (- 1 + x) (y + 3) (y^{2} - 3 y + 9)

Solution steps

(x y)^{3} - 27 - y^{3} + 27 x^{3}

Factor

(x y)^{3} - y^{3} : y^{3} (x - 1) (x^{2} + x + 1)

Factor

- 27 + 27 x^{3} : 27 (x - 1) (x^{2} + x + 1)

= y^{3} (x - 1) (x^{2} + x + 1) + 27 (x - 1) (x^{2} + x + 1)

Factor out common term

(x^{2} + 1 + x) (- 1 + x)

= (x^{2} + 1 + x) (- 1 + x) (y^{3} + 27)

Factor

y^{3} + 27 : (y + 3) (y^{2} - 3 y + 9)

= (y + 3) (x - 1) (x^{2} + x + 1) (y^{2} - 3 y + 9)

- \frac{1}{5 ( 3 ( 1 ) + 2 ) ^{2}}

145 b^{2} + 29 b

\frac{5 ( b ) ^{2}}{5 b ^{5}}

- 6 x + 9 = 33

5 \cdot 2

What is factor (x*y)^3-27-y^3+27x^3 ?
The solution to factor (x*y)^3-27-y^3+27x^3 is (x^2+1+x)(-1+x)(y+3)(y^2-3y+9)