What is factor r^3w^6-125p^{12} ?

The solution to factor r^3w^6-125p^{12} is (rw^2-5p^4)(r^2w^4+5rw^2p^4+25p^8)

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factor r^3w^6-125p^{12}

factor

r^{3} w^{6} - 125 p^{12}

(r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})

Solution steps

r^{3} w^{6} - 125 p^{12}

Rewrite

r^{3} w^{6}

(r w^{2})^{3}

Rewrite

125 p^{12}

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

= (r w^{2})^{3} - (5 p^{4})^{3}

Apply Difference of Cubes Formula:

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

(r w^{2})^{3} - (5 p^{4})^{3} = (r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} 5 p^{4} + (5 p^{4})^{2})

= (r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} 5 p^{4} + (5 p^{4})^{2})

Simplify

(r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} \cdot 5 p^{4} + (5 p^{4})^{2}) : (r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})

= (r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})

x \frac{d y}{d x} - 2 x y

4 x^{6} - 9 y^{1} 0 z^{1} 2

(sin (5 x))^{4}

(y + z)^{3} - 125

(x + y)^{3} + 216

What is factor r^3w^6-125p^{12} ?
The solution to factor r^3w^6-125p^{12} is (rw^2-5p^4)(r^2w^4+5rw^2p^4+25p^8)