Solve x+x-x*x+x+x-x*x*x+x*x

$$x + x - x \cdot x + x + x - x \cdot x \cdot x + x \cdot x$$

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

$$x+x-x^{2}+x+x-xxx+xx$$

Multiply x and x to get x^{2}.

$$x+x-x^{2}+x+x-x^{2}x+xx$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply x and x to get x^{2}.

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

Combine x and x to get 2x.

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

Combine 2x and x to get 3x.

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

Combine 3x and x to get 4x.

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

Combine -x^{2} and x^{2} to get 0.

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

Factor

$$x\left(-x-2\right)\left(x-2\right)$$

Solution Steps

Factor out x.

$$x\left(4-xx\right)$$

Consider 1+1-x+1+1-x^{2}+x. Multiply and combine like terms.

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

Consider -x^{2}+4. Rewrite -x^{2}+4 as 2^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2-x\right)\left(2+x\right)$$

Reorder the terms.

$$\left(-x+2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$x\left(-x+2\right)\left(x+2\right)$$