What is factor 216a^3+b^6c^9 ?

The solution to factor 216a^3+b^6c^9 is (6a+b^2c^3)(36a^2-6ab^2c^3+b^4c^6)

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factor 216a^3+b^6c^9

factor

216 a^{3} + b^{6} c^{9}

(6 a + b^{2} c^{3}) (36 a^{2} - 6 a b^{2} c^{3} + b^{4} c^{6})

Solution steps

216 a^{3} + b^{6} c^{9}

Rewrite

216 a^{3}

(6 a)^{3}

Rewrite

b^{6} c^{9}

(b^{2} c^{3})^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(6 a + b^{2} c^{3}) ((6 a)^{2} - 6 a b^{2} c^{3} + (b^{2} c^{3})^{2}) : (6 a + b^{2} c^{3}) (36 a^{2} - 6 a b^{2} c^{3} + b^{4} c^{6})

= (6 a + b^{2} c^{3}) (36 a^{2} - 6 a b^{2} c^{3} + b^{4} c^{6})

(6 x - 1) + (- x^{2})

(x^{- 1} + y^{- 1})^{2}

a^{4} + 6^{2} + 1

(x^{2} y^{4}) 2

(x - y)^{3} - 8

What is factor 216a^3+b^6c^9 ?
The solution to factor 216a^3+b^6c^9 is (6a+b^2c^3)(36a^2-6ab^2c^3+b^4c^6)