What is factor 27x^3-1000y^3 ?

The solution to factor 27x^3-1000y^3 is (3x-10y)(9x^2+30xy+100y^2)

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factor 27x^3-1000y^3

factor

27 x^{3} - 1000 y^{3}

(3 x - 10 y) (9 x^{2} + 30 x y + 100 y^{2})

Solution steps

27 x^{3} - 1000 y^{3}

Apply exponent rules

= (3 x)^{3} - (10 y)^{3}

Apply Difference of Cubes Formula:

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

(3 x)^{3} - (10 y)^{3} = (3 x - 10 y) ((3 x)^{2} + 3 x \cdot 10 y + (10 y)^{2})

= (3 x - 10 y) ((3 x)^{2} + 3 x \cdot 10 y + (10 y)^{2})

Simplify

(3 x)^{2} + 3 x \cdot 10 y + (10 y)^{2} : 9 x^{2} + 30 x y + 100 y^{2}

= (3 x - 10 y) (9 x^{2} + 30 x y + 100 y^{2})

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

- 4 < \frac{6 x - 9}{9} < 4

(x + 1) (x - 2) < 0

5 n^{2} + 19 n + 12

\frac{2 ( 2 ) ^{\frac{3}{2}}}{3}

What is factor 27x^3-1000y^3 ?
The solution to factor 27x^3-1000y^3 is (3x-10y)(9x^2+30xy+100y^2)