Solve x^2+3x+3x+9

$${ x }^{ 2 } +3x+3x+9$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$x^{2}+6x+9$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+9. To find a and b, set up a system to be solved.

$$a+b=6 ab=1\times 9=9$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 9.

$$1,9 3,3$$

Calculate the sum for each pair.

$$1+9=10 3+3=6$$

The solution is the pair that gives sum 6.

$$a=3 b=3$$

Rewrite x^{2}+6x+9 as \left(x^{2}+3x\right)+\left(3x+9\right).

$$\left(x^{2}+3x\right)+\left(3x+9\right)$$

Factor out x in the first and 3 in the second group.

$$x\left(x+3\right)+3\left(x+3\right)$$

Factor out common term x+3 by using distributive property.

$$\left(x+3\right)\left(x+3\right)$$

Rewrite as a binomial square.

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

Evaluate

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

Solution Steps

Combine 3x and 3x to get 6x.

$$x^{2}+6x+9$$