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

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

Evaluate

$$2x^{4}-2x^{3}+x^{2}+2x-1$$

Solution Steps

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

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

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

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

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

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

To find the opposite of 2x^{3}-2x, find the opposite of each term.

$$2x^{4}+x^{2}-1-2x^{3}+2x$$

Expand

$$2x^{4}-2x^{3}+x^{2}+2x-1$$

Solution Steps

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

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

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

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

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

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

To find the opposite of 2x^{3}-2x, find the opposite of each term.

$$2x^{4}+x^{2}-1-2x^{3}+2x$$