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 Sum 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})

(x^{2})^{- 6}

6 x^{2} - 31 x y + 18 y^{2}

2 (3^{a}) + (3^{a})

(a + 2 b)^{10}

9 x^{2} - 21 x y + 10 y^{2}

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