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 Difference 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})

k^{2} + (k + 1)

3 ab + 3 a c + 5 b d + 5 c d

5 c + 10 a - b c - 2 ab

5 x^{3} + 2 x^{2} 15 + 6

7 a x - 7 b x - 4 a y + 4 b y

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)