Answer :

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.