What is factor 27u^3-125v^3 ?

The solution to factor 27u^3-125v^3 is (3u-5v)(9u^2+15uv+25v^2)

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factor 27u^3-125v^3

factor

27 u^{3} - 125 v^{3}

(3 u - 5 v) (9 u^{2} + 15 uv + 25 v^{2})

Solution steps

27 u^{3} - 125 v^{3}

Apply exponent rules

= (3 u)^{3} - (5 v)^{3}

Apply Difference of Cubes Formula:

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

(3 u)^{3} - (5 v)^{3} = (3 u - 5 v) ((3 u)^{2} + 3 u \cdot 5 v + (5 v)^{2})

= (3 u - 5 v) ((3 u)^{2} + 3 u \cdot 5 v + (5 v)^{2})

Simplify

(3 u)^{2} + 3 u \cdot 5 v + (5 v)^{2} : 9 u^{2} + 15 uv + 25 v^{2}

= (3 u - 5 v) (9 u^{2} + 15 uv + 25 v^{2})

x^{2} - 4 x - 100 = 0

20 + 10 a \geq - 20

4 w^{3} - 9 w

7 x + 4 = 39

16 x^{4} - 625 y^{4}

What is factor 27u^3-125v^3 ?
The solution to factor 27u^3-125v^3 is (3u-5v)(9u^2+15uv+25v^2)