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

$$\frac{ x-1 }{ 2 } (2x- \frac{ x-1 }{ 2 } \times 2)( { x }^{ 2 } +x-(x-1))$$

Evaluate

$$\frac{x^{4}-1}{2}$$

Solution Steps

Cancel out 2 and 2.

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

To find the opposite of x-1, find the opposite of each term.

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

Combine 2x and -x to get x.

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

To find the opposite of x-1, find the opposite of each term.

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

Combine x and -x to get 0.

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

Express \frac{x-1}{2}\left(x+1\right) as a single fraction.

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

Express \frac{\left(x-1\right)\left(x+1\right)}{2}\left(x^{2}+1\right) as a single fraction.

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

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

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

Consider \left(x^{2}-1\right)\left(x^{2}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{x^{4}-1}{2}$$

Expand

$$\frac{x^{4}-1}{2}$$

Solution Steps

Cancel out 2 and 2.

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

To find the opposite of x-1, find the opposite of each term.

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

Combine 2x and -x to get x.

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

To find the opposite of x-1, find the opposite of each term.

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

Combine x and -x to get 0.

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

Express \frac{x-1}{2}\left(x+1\right) as a single fraction.

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

Express \frac{\left(x-1\right)\left(x+1\right)}{2}\left(x^{2}+1\right) as a single fraction.

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

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

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

Consider \left(x^{2}-1\right)\left(x^{2}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{x^{4}-1}{2}$$