Solve [(2x^2+x)(x+x^2):x+1x+x^2]:(2x)

$$[ ( 2 x ^ { 2 } + x ) ( x + x ^ { 2 } ) : x + 1 x + x ^ { 2 } ] : ( 2 x )$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(2x^{2}+x\right)\left(x+x^{2}\right)}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{3}+3x^{2}+x+1x+x^{2}}{2x}$$

Combine x and 1x to get 2x.

$$\frac{2x^{3}+3x^{2}+2x+x^{2}}{2x}$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$\frac{2x^{3}+4x^{2}+2x}{2x}$$

Factor the expressions that are not already factored.

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

Cancel out 2x in both numerator and denominator.

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

Expand the expression.

$$x^{2}+2x+1$$

Expand

$$x^{2}+2x+1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(2x^{2}+x\right)\left(x+x^{2}\right)}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{3}+3x^{2}+x+1x+x^{2}}{2x}$$

Combine x and 1x to get 2x.

$$\frac{2x^{3}+3x^{2}+2x+x^{2}}{2x}$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$\frac{2x^{3}+4x^{2}+2x}{2x}$$

Factor the expressions that are not already factored.

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

Cancel out 2x in both numerator and denominator.

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

Expand the expression.

$$x^{2}+2x+1$$