What is factor a^3b^3-x^6 ?

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

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factor a^3b^3-x^6

factor

a^{3} b^{3} - x^{6}

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

Solution steps

a^{3} b^{3} - x^{6}

Rewrite

a^{3} b^{3}

(ab)^{3}

= (ab)^{3} - x^{6}

Apply exponent rule:

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

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

= (ab)^{3} - (x^{2})^{3}

Apply Difference of Cubes Formula:

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

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

= (ab - x^{2}) (x^{4} + x^{2} ab + (ab)^{2})

Simplify

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

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

∣ 2 x + 1 ∣ > 7

∣ x - 5 ∣ = 2 x + 3

28 n^{2} = - 96 - 184 n

1 + \frac{1}{2} + \frac{1}{3}

4 x (x + 3) \geq - 9

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