What is factor 216c^{15}-125a^3b^9 ?

The solution to factor 216c^{15}-125a^3b^9 is (6c^5-5ab^3)(36c^{10}+30c^5ab^3+25a^2b^6)

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factor 216c^{15}-125a^3b^9

factor

216 c^{15} - 125 a^{3} b^{9}

(6 c^{5} - 5 a b^{3}) (36 c^{10} + 30 c^{5} a b^{3} + 25 a^{2} b^{6})

Solution steps

216 c^{15} - 125 a^{3} b^{9}

Rewrite

216 c^{15}

(6 c^{5})^{3}

Rewrite

125 a^{3} b^{9}

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

= (6 c^{5})^{3} - (5 a b^{3})^{3}

Apply Difference of Cubes Formula:

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

(6 c^{5})^{3} - (5 a b^{3})^{3} = (6 c^{5} - 5 a b^{3}) ((6 c^{5})^{2} + 6 c^{5} 5 a b^{3} + (5 a b^{3})^{2})

= (6 c^{5} - 5 a b^{3}) ((6 c^{5})^{2} + 6 c^{5} 5 a b^{3} + (5 a b^{3})^{2})

Simplify

(6 c^{5} - 5 a b^{3}) ((6 c^{5})^{2} + 6 c^{5} \cdot 5 a b^{3} + (5 a b^{3})^{2}) : (6 c^{5} - 5 a b^{3}) (36 c^{10} + 30 c^{5} a b^{3} + 25 a^{2} b^{6})

= (6 c^{5} - 5 a b^{3}) (36 c^{10} + 30 c^{5} a b^{3} + 25 a^{2} b^{6})

+ 10 w^{2} - 31 w + 15

4 x^{3} + 4 x y d x

2 ab + 2 c d + 4 a c + b d

(- 7 x) + (18 x^{2})

15 e^{2} + 2 e - 1

What is factor 216c^{15}-125a^3b^9 ?
The solution to factor 216c^{15}-125a^3b^9 is (6c^5-5ab^3)(36c^{10}+30c^5ab^3+25a^2b^6)