What is factor 125x^3-27y^3 ?

The solution to factor 125x^3-27y^3 is (5x-3y)(25x^2+15xy+9y^2)

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factor 125x^3-27y^3

factor

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

(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2})

Solution steps

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

Apply exponent rules

= (5 x)^{3} - (3 y)^{3}

Apply Difference of Cubes Formula:

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

(5 x)^{3} - (3 y)^{3} = (5 x - 3 y) ((5 x)^{2} + 5 x \cdot 3 y + (3 y)^{2})

= (5 x - 3 y) ((5 x)^{2} + 5 x \cdot 3 y + (3 y)^{2})

Simplify

(5 x)^{2} + 5 x \cdot 3 y + (3 y)^{2} : 25 x^{2} + 15 x y + 9 y^{2}

= (5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2})

z^{2} + 8 z - 20

2 (- 2)^{3} + 3 (- 2)^{2} - 12 (- 2) + 1

\frac{x + 2}{x + 3} - \frac{x - 1}{x - 2} < 0

∣ x - 4 ∣ < 0

4 x^{2} = - 32 x

What is factor 125x^3-27y^3 ?
The solution to factor 125x^3-27y^3 is (5x-3y)(25x^2+15xy+9y^2)