What is factor x^6-b^9 ?

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

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factor x^6-b^9

factor

x^{6} - b^{9}

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

Solution steps

x^{6} - b^{9}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(x^{2})^{2} + x^{2} b^{3} + (b^{3})^{2} : x^{4} + x^{2} b^{3} + b^{6}

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

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

(12 m)^{\frac{1}{3}}

\frac{3}{8} + \frac{5}{6}

10 0^{- \frac{3}{2}}

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

∣ x - 5 ∣ = 0.04

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