What is factor 8s^3t^6+125q^3 ?

The solution to factor 8s^3t^6+125q^3 is (2st^2+5q)(4s^2t^4-10st^2q+25q^2)

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factor 8s^3t^6+125q^3

factor

8 s^{3} t^{6} + 125 q^{3}

(2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})

Solution steps

8 s^{3} t^{6} + 125 q^{3}

Rewrite

8 s^{3} t^{6}

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

Rewrite

125 q^{3}

(5 q)^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(2 s t^{2} + 5 q) ((2 s t^{2})^{2} - 2 s t^{2} \cdot 5 q + (5 q)^{2}) : (2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})

= (2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})

10 - 25

- 4 + (- 6 p)

8 (x + y)^{3} - y^{3}

ln (3) (3)

216 - x^{15}

What is factor 8s^3t^6+125q^3 ?
The solution to factor 8s^3t^6+125q^3 is (2st^2+5q)(4s^2t^4-10st^2q+25q^2)