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

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

Evaluate

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

Solution Steps

Add 1 and 3 to get 4.

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

Subtract 3 from 1 to get -2.

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

The opposite of -2 is 2.

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

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

$$\left(x^{3}-3x^{2}-6x+8\right)\left(x+2\right)$$

Use the distributive property to multiply x^{3}-3x^{2}-6x+8 by x+2 and combine like terms.

$$x^{4}-x^{3}-12x^{2}-4x+16$$

Expand

$$x^{4}-x^{3}-12x^{2}-4x+16$$

Solution Steps

Add 1 and 3 to get 4.

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

Subtract 3 from 1 to get -2.

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

The opposite of -2 is 2.

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

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

$$\left(x^{3}-3x^{2}-6x+8\right)\left(x+2\right)$$

Use the distributive property to multiply x^{3}-3x^{2}-6x+8 by x+2 and combine like terms.

$$x^{4}-x^{3}-12x^{2}-4x+16$$