Certainly! Let's solve the given expression step-by-step.
1. Identify the components:
The given expression is [tex]\( x^2 + \square x^2 + 36 \)[/tex]. Here, we need to figure out what goes into the box (represented as [tex]\(\square\)[/tex]).
2. Introduce a variable:
We'll represent the boxed value with a variable, say [tex]\(a\)[/tex]. Thus, the expression becomes:
[tex]\[
x^2 + ax^2 + 36
\][/tex]
3. Combine like terms:
Notice that [tex]\( x^2 \)[/tex] terms can be combined. The like terms here are [tex]\( x^2 \)[/tex] and [tex]\( ax^2 \)[/tex]. When we combine these, we get:
[tex]\[
(1 + a)x^2 + 36
\][/tex]
4. Final expression:
So, the simplified expression after introducing the variable [tex]\(a\)[/tex] in place of the box and combining the like terms is:
[tex]\[
x^2 + ax^2 + 36
\][/tex]
Therefore, the expression simplifies to [tex]\(x^2 + ax^2 + 36\)[/tex].
