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

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

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factor 125v^3-27w^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

\frac{48}{8}

\frac{3 + 2 i}{5 - 4 i}

\frac{4 ( v ^{3} ) ^{2}}{2 v ^{5}}

3 \frac{1}{4} - 2 \frac{7}{8}

\frac{- 14}{2}

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