What is factor 125x^3y^6z^{12}-d^9 ?

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

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factor 125x^3y^6z^{12}-d^9

factor

125 x^{3} y^{6} z^{12} - d^{9}

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

Solution steps

125 x^{3} y^{6} z^{12} - d^{9}

Rewrite

125 x^{3} y^{6} z^{12}

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

= (5 x y^{2} z^{4})^{3} - d^{9}

Apply exponent rule:

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

d^{9} = (d^{3})^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

2^{\frac{1}{2}} \cdot 725 + 1200

in (2.3)

I m (z)^{3}

3 x^{2 + 4 x - 5}

49 a^{10 n + 6 m} - b^{2 b - 8}

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