What is factor x^{15}-125y^3 ?

The solution to factor x^{15}-125y^3 is (x^5-5y)(x^{10}+5x^5y+25y^2)

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factor x^{15}-125y^3

factor

x^{15} - 125 y^{3}

(x^{5} - 5 y) (x^{10} + 5 x^{5} y + 25 y^{2})

Solution steps

x^{15} - 125 y^{3}

Apply exponent rules

= (x^{5})^{3} - (5 y)^{3}

Apply Difference of Cubes Formula:

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

(x^{5})^{3} - (5 y)^{3} = (x^{5} - 5 y) ((x^{5})^{2} + x^{5} \cdot 5 y + (5 y)^{2})

= (x^{5} - 5 y) ((x^{5})^{2} + x^{5} \cdot 5 y + (5 y)^{2})

Simplify

(x^{5})^{2} + x^{5} \cdot 5 y + (5 y)^{2} : x^{10} + 5 x^{5} y + 25 y^{2}

= (x^{5} - 5 y) (x^{10} + 5 x^{5} y + 25 y^{2})

\frac{5 x}{3} \geq \frac{3 ( 3 - x )}{4}

e^{x} < 0

- 16 > 5 + 7 x

(\frac{1}{6} + \frac{1}{3} \cdot - x^{6} + x^{4}) > 0

What is factor x^{15}-125y^3 ?
The solution to factor x^{15}-125y^3 is (x^5-5y)(x^{10}+5x^5y+25y^2)