Solve 2left(x^3+2x-1right)^2-1left(x^3+2x-1right)

$$2 { \left( { x }^{ 3 } +2x-1 \right) }^{ 2-1 } \left( { x }^{ 3 } +2x-1 \right)$$

Evaluate

$$2\left(x^{3}+2x-1\right)^{2}$$

Solution Steps

Subtract 1 from 2 to get 1.

$$2\left(x^{3}+2x-1\right)^{1}\left(x^{3}+2x-1\right)$$

Calculate x^{3}+2x-1 to the power of 1 and get x^{3}+2x-1.

$$2\left(x^{3}+2x-1\right)\left(x^{3}+2x-1\right)$$

Multiply x^{3}+2x-1 and x^{3}+2x-1 to get \left(x^{3}+2x-1\right)^{2}.

$$2\left(x^{3}+2x-1\right)^{2}$$

Square x^{3}+2x-1.

$$2\left(x^{6}+4x^{4}-2x^{3}+4x^{2}-4x+1\right)$$

Use the distributive property to multiply 2 by x^{6}+4x^{4}-2x^{3}+4x^{2}-4x+1.

$$2x^{6}+8x^{4}-4x^{3}+8x^{2}-8x+2$$

Differentiate w.r.t. x

$$4\left(3x^{2}+2\right)\left(x^{3}+2x-1\right)$$