Solve x^2+x+x+1

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+1. To find a and b, set up a system to be solved.

$$a+b=2 ab=1\times 1=1$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=1$$

Rewrite x^{2}+2x+1 as \left(x^{2}+x\right)+\left(x+1\right).

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

Factor out x in x^{2}+x.

$$x\left(x+1\right)+x+1$$

Factor out common term x+1 by using distributive property.

$$\left(x+1\right)\left(x+1\right)$$

Rewrite as a binomial square.

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

Evaluate

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

Solution Steps

Combine x and x to get 2x.

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