Factor x^2+6x+9

Problem

$x^2+6x+9$

Solution

1. Identify the form of the quadratic expression $a{x}^2+bx+c$ where $a=1$ $b=6$ and $c=9$

2. Recognize that the expression is a perfect square trinomial because the first term $x^2$ is ${\left(x\right)}^2$ the last term $9$ is ${\left(3\right)}^2$ and the middle term $6x$ is $2\left(x\right)\left(3\right)$

3. Apply the formula for a perfect square trinomial, which states $a^2+2ab+b^2={(a+b)}^2$

4. Substitute $a=x$ and $b=3$ into the formula to get ${(x+3)}^2$

Final Answer

$x^2+6x+9={(x+3)}^2$

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