What is factor a^6-b^9 ?

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

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factor a^6-b^9

factor

a^{6} - b^{9}

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

Solution steps

a^{6} - b^{9}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

x^{4} + x y^{3} + x^{3} + y^{3}

(a + 8)^{3}

\frac{cos ( lo g _{10} ( x ^{2} ) )}{x ^{4}}

(i) (2 x + 1)^{3}

(x + 3)^{6} cos (\frac{1}{( x + 3 ) ^{2}})

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