Q. \((x+3)^2\)

We are asked to simplify the expression \((x+3)(x+3)\). This means we multiply the two binomials together.

Step 1: Recognize the expression

The expression \((x+3)(x+3)\) is the same factor written twice. So it is a “square of a binomial.” We can treat it like \((x+3)^2\).

Step 2: Use the distributive property (FOIL)

Multiply each term in the first parentheses by each term in the second parentheses:

\((x+3)(x+3)\) has these products:

• \(x \cdot x = x^2\)
• \(x \cdot 3 = 3x\)
• \(3 \cdot x = 3x\)
• \(3 \cdot 3 = 9\)

Step 3: Write all the terms together

Add the results from all four products:

\[
\begin{aligned}
(x+3)(x+3) &= x^2 + 3x + 3x + 9
\end{aligned}
\]

Step 4: Combine like terms

The like terms are \(3x\) and \(3x\). Combine them:

\[
\begin{aligned}
x^2 + 3x + 3x + 9 &= x^2 + 6x + 9
\end{aligned}
\]

Final Answer

\[
(x+3)(x+3) = x^2 + 6x + 9
\]