What is factor 27x^3-(x-y)^9 ?

The solution to factor 27x^3-(x-y)^9 is (3x-x^3+3x^2y-3xy^2+y^3)(9x^2+3x(x-y)^3+(x-y)^6)

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factor 27x^3-(x-y)^9

factor

27 x^{3} - (x - y)^{9}

(3 x - x^{3} + 3 x^{2} y - 3 x y^{2} + y^{3}) (9 x^{2} + 3 x (x - y)^{3} + (x - y)^{6})

Solution steps

27 x^{3} - (x - y)^{9}

Rewrite

27 x^{3} - (x - y)^{9}

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

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

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

Refine

= (3 x - (x - y)^{3}) (9 x^{2} + 3 x (x - y)^{3} + (x - y)^{6})

Expand

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

= (- x^{3} + 3 x^{2} y + 3 x - 3 x y^{2} + y^{3}) (9 x^{2} + 3 x (x - y)^{3} + (x - y)^{6})

9 72 + 32

3^{2} - 12

[5.1]

- 8 + 83 i

4 p + 8 r - pq - 2 q r

What is factor 27x^3-(x-y)^9 ?
The solution to factor 27x^3-(x-y)^9 is (3x-x^3+3x^2y-3xy^2+y^3)(9x^2+3x(x-y)^3+(x-y)^6)