Certainly! Let's work through the provided expression step-by-step:
Given the expression:
[tex]\[
(a+b)^2 - 11(a+b) - 42
\][/tex]
1. First, let's expand [tex]\((a+b)^2\)[/tex]:
[tex]\[
(a+b)^2 = a^2 + 2ab + b^2
\][/tex]
So now, our expression becomes:
[tex]\[
a^2 + 2ab + b^2 - 11(a+b) - 42
\][/tex]
2. Next, distribute the [tex]\(-11\)[/tex] across [tex]\((a+b)\)[/tex]:
[tex]\[
-11(a+b) = -11a - 11b
\][/tex]
Substituting this back into the expression, we get:
[tex]\[
a^2 + 2ab + b^2 - 11a - 11b - 42
\][/tex]
3. The terms are already simplified; therefore, our final simplified polynomial expression is:
[tex]\[
a^2 + 2ab + b^2 - 11a - 11b - 42
\][/tex]
So, the simplified form of [tex]\((a+b)^2 - 11(a+b) - 42\)[/tex] is:
[tex]\[
a^2 + 2ab + b^2 - 11a - 11b - 42
\][/tex]
This is the expanded and simplified form of the given expression.
