What is factor a^3b^3-c^{12} ?

The solution to factor a^3b^3-c^{12} is (ab-c^4)(a^2b^2+abc^4+c^8)

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factor a^3b^3-c^{12}

factor

a^{3} b^{3} - c^{12}

(ab - c^{4}) (a^{2} b^{2} + ab c^{4} + c^{8})

Solution steps

a^{3} b^{3} - c^{12}

Rewrite

a^{3} b^{3}

(ab)^{3}

= (ab)^{3} - c^{12}

Apply exponent rule:

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

c^{12} = (c^{4})^{3}

= (ab)^{3} - (c^{4})^{3}

Apply Difference of Cubes Formula:

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

(ab)^{3} - (c^{4})^{3} = (ab - c^{4}) ((ab)^{2} + ab c^{4} + c^{8})

= (ab - c^{4}) ((ab)^{2} + c^{4} ab + c^{8})

Simplify

(ab - c^{4}) ((ab)^{2} + ab c^{4} + c^{8}) : (ab - c^{4}) (a^{2} b^{2} + ab c^{4} + c^{8})

= (ab - c^{4}) (a^{2} b^{2} + ab c^{4} + c^{8})

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What is factor a^3b^3-c^{12} ?
The solution to factor a^3b^3-c^{12} is (ab-c^4)(a^2b^2+abc^4+c^8)