What is factor 8e^3f^6-125g^3 ?

The solution to factor 8e^3f^6-125g^3 is (2ef^2-5g)(4e^2f^4+10ef^2g+25g^2)

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factor 8e^3f^6-125g^3

factor

8 e^{3} f^{6} - 125 g^{3}

(2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

Solution steps

8 e^{3} f^{6} - 125 g^{3}

Rewrite

8 e^{3} f^{6}

(2 e f^{2})^{3}

Rewrite

125 g^{3}

(5 g)^{3}

= (2 e f^{2})^{3} - (5 g)^{3}

Apply Difference of Cubes Formula:

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

(2 e f^{2})^{3} - (5 g)^{3} = (2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} 5 g + (5 g)^{2})

= (2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} 5 g + (5 g)^{2})

Simplify

(2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} \cdot 5 g + (5 g)^{2}) : (2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

= (2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

(cos (11 x))^{2}

e^{5} - e^{3}

r (24 π)

+ (- 5)

cos^{6} (θ) + sin^{6} (θ)

What is factor 8e^3f^6-125g^3 ?
The solution to factor 8e^3f^6-125g^3 is (2ef^2-5g)(4e^2f^4+10ef^2g+25g^2)