# How do you find the product (x+3)(x+3)?

May 9, 2017

See a solution process below:

#### Explanation:

This is a special form of quadratic where:

(a + b)^2 = a^2 + 2ab + b^

Substituting $x$ for $a$ and $3$ for $b$ gives:

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

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

If you want to multiply out the long way you can use this process. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{x} + \textcolor{red}{3}\right) \left(\textcolor{b l u e}{x} + \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{3}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{3}\right)$

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

We can now combine like terms:

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

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

The same result as above.