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

The solution to factor 27x^3-(x-y)^3 is (2x+y)(13x^2-5xy+y^2)

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

factor

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

(2 x + y) (13 x^{2} - 5 x y + y^{2})

Solution steps

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

Rewrite

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

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

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

9 x^{2} + 3 x (x - y) + (x - y)^{2} : 13 x^{2} - 5 x y + y^{2}

= (2 x + y) (13 x^{2} - 5 x y + y^{2})

a y - 5 b y + 5 a x - 25 b x

[- 9.8]

6 x y - 5 z + 2 y - 15 x z

3 a^{2} + 6 a d + ab + 2 b d

π r^{2} h - π r^{2} h

What is factor 27x^3-(x-y)^3 ?
The solution to factor 27x^3-(x-y)^3 is (2x+y)(13x^2-5xy+y^2)