What is factor 27a^3+125b^3 ?

The solution to factor 27a^3+125b^3 is (3a+5b)(9a^2-15ab+25b^2)

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factor 27a^3+125b^3

factor

27 a^{3} + 125 b^{3}

(3 a + 5 b) (9 a^{2} - 15 ab + 25 b^{2})

Solution steps

27 a^{3} + 125 b^{3}

Apply exponent rules

= (3 a)^{3} + (5 b)^{3}

Apply Sum of Cubes Formula:

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

(3 a)^{3} + (5 b)^{3} = (3 a + 5 b) ((3 a)^{2} - 3 a \cdot 5 b + (5 b)^{2})

= (3 a + 5 b) ((3 a)^{2} - 3 a \cdot 5 b + (5 b)^{2})

Simplify

(3 a)^{2} - 3 a \cdot 5 b + (5 b)^{2} : 9 a^{2} - 15 ab + 25 b^{2}

= (3 a + 5 b) (9 a^{2} - 15 ab + 25 b^{2})

(a + 7)^{3}

\frac{( 5 x ^{2} - 33 x - 14 )}{( x ^{2} - 7 x )}

(y^{5})^{4}

(a - 6)^{3}

8 (a + 1)^{3} - 1

What is factor 27a^3+125b^3 ?
The solution to factor 27a^3+125b^3 is (3a+5b)(9a^2-15ab+25b^2)