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

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

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factor a^3b^6+c^9

factor

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

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

Solution steps

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

Rewrite

a^{3} b^{6}

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

= (a b^{2})^{3} + c^{9}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

c^{9} = (c^{3})^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

(x + 4) - x^{3} - 3 x^{2}

\frac{a ^{2}}{4} - b^{2}

3 x - 9 y - x z + 3 yz

(3 a)^{2} + 10 ab + (7 b)^{2}

sin^{2} (x) - 3 sin (x) - 40

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