Solve G(x)=2(x-1)^2(x^2+1)

$$G ( x ) = 2 ( x - 1 ) ^ { 2 } ( x ^ { 2 } + 1 )$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

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

Use the distributive property to multiply 2x^{2}-4x+2 by x^{2}+1 and combine like terms.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

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

Use the distributive property to multiply 2x^{2}-4x+2 by x^{2}+1 and combine like terms.

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