To expand the expression \((x + 6)(x + 6)\), we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
Here are the steps:
-
First terms: Multiply the first terms in each binomial:
\[ x \cdot x = x^2 \] -
Outer terms: Multiply the outer terms:
\[ x \cdot 6 = 6x \] -
Inner terms: Multiply the inner terms:
\[ 6 \cdot x = 6x \] -
Last terms: Multiply the last terms in each binomial:
\[ 6 \cdot 6 = 36 \]
Next, we combine all of the results together:
\[
x^2 + 6x + 6x + 36
\]
Now, combine like terms (the \(6x\) and \(6x\)):
\[
x^2 + 12x + 36
\]
Thus, the expanded expression is:
\[
\boxed{x^2 + 12x + 36}
\]