What is factor 1000x^6y^{12}-1 ?

The solution to factor 1000x^6y^{12}-1 is (10x^2y^4-1)(100x^4y^8+10x^2y^4+1)

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factor 1000x^6y^{12}-1

factor

1000 x^{6} y^{12} - 1

(10 x^{2} y^{4} - 1) (100 x^{4} y^{8} + 10 x^{2} y^{4} + 1)

Solution steps

1000 x^{6} y^{12} - 1

Apply exponent rules

= (10 x^{2} y^{4})^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

(10 x^{2} y^{4})^{3} - 1^{3} = (10 x^{2} y^{4} - 1) ((10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2})

= (10 x^{2} y^{4} - 1) ((10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2})

Simplify

(10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2} : 100 x^{4} y^{8} + 10 x^{2} y^{4} + 1

= (10 x^{2} y^{4} - 1) (100 x^{4} y^{8} + 10 x^{2} y^{4} + 1)

1 \frac{5}{8} + \frac{3}{4}

x (- 2)

- 3108 + 43

\frac{- 3 x}{2 x ^{2} - 8 x}

\frac{2 - i}{5 i}

What is factor 1000x^6y^{12}-1 ?
The solution to factor 1000x^6y^{12}-1 is (10x^2y^4-1)(100x^4y^8+10x^2y^4+1)