What is factor 125x^3-8y^3 ?

The solution to factor 125x^3-8y^3 is (5x-2y)(25x^2+10xy+4y^2)

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factor 125x^3-8y^3

factor

125 x^{3} - 8 y^{3}

(5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})

Solution steps

125 x^{3} - 8 y^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(5 x)^{2} + 5 x \cdot 2 y + (2 y)^{2} : 25 x^{2} + 10 x y + 4 y^{2}

= (5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})

4 x^{2} - 1 = 0

(x - 2)^{2} + 48 = (2 - 3 x)^{2}

(14 - 3) (12 + 7)

- x^{2} + 2 x + 2 = 0

16 x^{2} - 3 = 8 x

What is factor 125x^3-8y^3 ?
The solution to factor 125x^3-8y^3 is (5x-2y)(25x^2+10xy+4y^2)