What is factor 1+512e^3x^3 ?

The solution to factor 1+512e^3x^3 is (8ex+1)(64e^2x^2-8ex+1)

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factor 1+512e^3x^3

factor

1 + 512 e^{3} x^{3}

(8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

Solution steps

1 + 512 e^{3} x^{3}

Rewrite

512 e^{3} x^{3}

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

= 1 + (2^{3} e x)^{3}

Rewrite

1

1^{3}

= (2^{3} e x)^{3} + 1^{3}

Apply Sum of Cubes Formula:

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

(2^{3} e x)^{3} + 1^{3} = (2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1)

= (2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1)

Simplify

(2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1) : (8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

= (8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

sin^{2} (4 t) s h^{2} (2 t)

cos (3 x^{2} + 3 x)

(x - 1)^{4} + (x - 1)^{2} - 6

x (3 t)

sin ({x})

What is factor 1+512e^3x^3 ?
The solution to factor 1+512e^3x^3 is (8ex+1)(64e^2x^2-8ex+1)