What is factor a^3b^6c^9-1 ?

The solution to factor a^3b^6c^9-1 is (ab^2c^3-1)(a^2b^4c^6+ab^2c^3+1)

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factor a^3b^6c^9-1

factor

a^{3} b^{6} c^{9} - 1

(a b^{2} c^{3} - 1) (a^{2} b^{4} c^{6} + a b^{2} c^{3} + 1)

Solution steps

a^{3} b^{6} c^{9} - 1

Rewrite

a^{3} b^{6} c^{9}

(a b^{2} c^{3})^{3}

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

Rewrite

1

1^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(a b^{2} c^{3} - 1) ((a b^{2} c^{3})^{2} + a b^{2} c^{3} + 1) : (a b^{2} c^{3} - 1) (a^{2} b^{4} c^{6} + a b^{2} c^{3} + 1)

= (a b^{2} c^{3} - 1) (a^{2} b^{4} c^{6} + a b^{2} c^{3} + 1)

ln (- 5 - 5 i)

(x + 5)^{2} - 8

5 - 0

(arcsin (3 x))^{4}

5 \frac{3}{6}

What is factor a^3b^6c^9-1 ?
The solution to factor a^3b^6c^9-1 is (ab^2c^3-1)(a^2b^4c^6+ab^2c^3+1)