What is factor x^6y^9-125z^{12} ?

The solution to factor x^6y^9-125z^{12} is (x^2y^3-5z^4)(x^4y^6+5x^2y^3z^4+25z^8)

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factor x^6y^9-125z^{12}

factor

x^{6} y^{9} - 125 z^{12}

(x^{2} y^{3} - 5 z^{4}) (x^{4} y^{6} + 5 x^{2} y^{3} z^{4} + 25 z^{8})

Solution steps

x^{6} y^{9} - 125 z^{12}

Rewrite

x^{6} y^{9}

(x^{2} y^{3})^{3}

Rewrite

125 z^{12}

(5 z^{4})^{3}

= (x^{2} y^{3})^{3} - (5 z^{4})^{3}

Apply Difference of Cubes Formula:

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

(x^{2} y^{3})^{3} - (5 z^{4})^{3} = (x^{2} y^{3} - 5 z^{4}) ((x^{2} y^{3})^{2} + 5 z^{4} x^{2} y^{3} + (5 z^{4})^{2})

= (x^{2} y^{3} - 5 z^{4}) ((5 z^{4})^{2} + 5 z^{4} x^{2} y^{3} + (x^{2} y^{3})^{2})

Simplify

(x^{2} y^{3} - 5 z^{4}) ((x^{2} y^{3})^{2} + 5 z^{4} x^{2} y^{3} + (5 z^{4})^{2}) : (x^{2} y^{3} - 5 z^{4}) (x^{4} y^{6} + 5 x^{2} y^{3} z^{4} + 25 z^{8})

= (x^{2} y^{3} - 5 z^{4}) (x^{4} y^{6} + 5 x^{2} y^{3} z^{4} + 25 z^{8})

24 p x + 8 x + 9 m p + 3 m - 15 p - 5

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

(6 x - x^{2}) - 8

10 x^{4} 8 x^{3}

sin^{5} (x) + cos^{5} (x)

What is factor x^6y^9-125z^{12} ?
The solution to factor x^6y^9-125z^{12} is (x^2y^3-5z^4)(x^4y^6+5x^2y^3z^4+25z^8)