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

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

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factor 27y^3-125z^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

ln (n^{2})

x + 3 y - 5 x

(2 a - 1)^{3}

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

(\frac{3 a + 1}{4 b})^{3}

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