What is factor 125x^9y^{18}-512z^{27} ?

The solution to factor 125x^9y^{18}-512z^{27} is (5x^3y^6-8z^9)(25x^6y^{12}+40x^3y^6z^9+64z^{18})

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factor 125x^9y^{18}-512z^{27}

factor

125 x^{9} y^{18} - 512 z^{27}

(5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})

Solution steps

125 x^{9} y^{18} - 512 z^{27}

Rewrite

125 x^{9} y^{18}

(5 x^{3} y^{6})^{3}

Rewrite

512 z^{27}

(2 z^{3})^{9}

= (5 x^{3} y^{6})^{3} - (2 z^{3})^{9}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

(2 z^{3})^{9} = ((2 z^{3})^{3})^{3}

= (5 x^{3} y^{6})^{3} - ((2 z^{3})^{3})^{3}

Apply Difference of Cubes Formula:

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

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

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

Simplify

(5 x^{3} y^{6} - (2 z^{3})^{3}) ((5 x^{3} y^{6})^{2} + (2 z^{3})^{3} \cdot 5 x^{3} y^{6} + (2 z^{3})^{6}) : (5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})

= (5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})

(x - y)^{2} + 6 (x - y) + 5

ln (e^{3} - e^{2})

(x + 3) 2 - 4 (x + 3)

(x)^{7}

3 x^{2} + 2 a x + (a^{2} - 6)

What is factor 125x^9y^{18}-512z^{27} ?
The solution to factor 125x^9y^{18}-512z^{27} is (5x^3y^6-8z^9)(25x^6y^{12}+40x^3y^6z^9+64z^{18})