What is factor a^6b^3-1 ?

The solution to factor a^6b^3-1 is (a^2b-1)(a^4b^2+a^2b+1)

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factor a^6b^3-1

factor

a^{6} b^{3} - 1

(a^{2} b - 1) (a^{4} b^{2} + a^{2} b + 1)

Solution steps

a^{6} b^{3} - 1

Apply exponent rules

= (a^{2} b)^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

(a^{2} b)^{3} - 1^{3} = (a^{2} b - 1) ((a^{2} b)^{2} + a^{2} b + 1^{2})

= (a^{2} b - 1) ((a^{2} b)^{2} + a^{2} b + 1^{2})

Simplify

(a^{2} b)^{2} + a^{2} b + 1^{2} : a^{4} b^{2} + a^{2} b + 1

= (a^{2} b - 1) (a^{4} b^{2} + a^{2} b + 1)

5 x - x y + 15 - 3 y

y^{2} + 9 x y

\frac{1}{( x - 3 )} + \frac{1}{x} - 9

5 - 5 x^{5} + 5

4 x^{2} - 28 x y + 49 y^{2}

What is factor a^6b^3-1 ?
The solution to factor a^6b^3-1 is (a^2b-1)(a^4b^2+a^2b+1)