What is factor 125q^6-r^6s^3 ?

The solution to factor 125q^6-r^6s^3 is (5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)

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factor 125q^6-r^6s^3

factor

125 q^{6} - r^{6} s^{3}

(5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})

Solution steps

125 q^{6} - r^{6} s^{3}

Rewrite

125 q^{6}

(5 q^{2})^{3}

Rewrite

r^{6} s^{3}

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

= (5 q^{2})^{3} - (r^{2} s)^{3}

Apply Difference of Cubes Formula:

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

(5 q^{2})^{3} - (r^{2} s)^{3} = (5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2})

= (5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2})

Simplify

(5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2}) : (5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})

= (5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})

10 x \leq - 7

36 x y^{5} m - 6 x y^{4} m^{6} + 42 x y^{3} m^{4}

\frac{1}{4} - \frac{1}{6} - \frac{1}{9} + \frac{1}{26}

2 (3 x - 4) = 22

25 x^{2} - 64 y^{2}

What is factor 125q^6-r^6s^3 ?
The solution to factor 125q^6-r^6s^3 is (5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)