What is factor x^3-2x^2y+3xy^2-6y^3 ?

The solution to factor x^3-2x^2y+3xy^2-6y^3 is (x-2y)(x^2+3y^2)

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factor x^3-2x^2y+3xy^2-6y^3

factor

x^{3} - 2 x^{2} y + 3 x y^{2} - 6 y^{3}

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

Solution steps

x^{3} - 2 x^{2} y + 3 x y^{2} - 6 y^{3}

= (x^{3} - 2 x^{2} y) + (3 x y^{2} - 6 y^{3})

Factor out

x^{2}

from

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

Factor out

3 y^{2}

from

3 x y^{2} - 6 y^{3} : 3 y^{2} (x - 2 y)

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

Factor out common term

x - 2 y

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

\frac{k + 3}{k} \cdot \frac{k ^{3} - 6 k ^{2} + 9 k}{k ^{2} - 9}

3 \cdot (2 x + 3 y)^{2} - 24 (2 x + 3 y) + 48

(2 x - 3)^{3} - 8 x + 12

b (2 a + a^{2} - 2 - a)

(a + b + c)^{2} + (a - b - c)^{2} + (b - c - a)^{2} + (c - b - a)^{2}

What is factor x^3-2x^2y+3xy^2-6y^3 ?
The solution to factor x^3-2x^2y+3xy^2-6y^3 is (x-2y)(x^2+3y^2)