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

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

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factor a^3b^6+c^6

factor

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

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

Solution steps

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

Rewrite

a^{3} b^{6}

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

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

Apply exponent rule:

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

c^{6} = (c^{2})^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

f (- ln (2))

a b^{2} + ab c + 3 b c + 3 c^{2}

9

cos (3 x^{2} - x)

\frac{- p + 1}{1 + p ^{2} - 2 p}

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