Let's break down and solve the problem step-by-step using algebraic techniques:
1. Identify the expressions:
- The first expression to consider is [tex]\(a^2 + b^2\)[/tex].
- The second expression to consider is [tex]\(a^2 - b^2\)[/tex].
2. Combine the expressions:
- We are required to find the sum of the two expressions: [tex]\(a^2 + b^2\)[/tex] and [tex]\(a^2 - b^2\)[/tex].
3. Write down the sum of the expressions:
[tex]\[
(a^2 + b^2) + (a^2 - b^2)
\][/tex]
4. Simplify the expression:
- Notice that when you add [tex]\(b^2\)[/tex] and [tex]\(-b^2\)[/tex], they cancel each other out.
- So the simplified form of the expression would just be:
[tex]\[
a^2 + b^2 + a^2 - b^2 = a^2 + a^2 = 2a^2
\][/tex]
5. Result:
- Thus, the result of adding [tex]\(a^2 + b^2\)[/tex] and [tex]\(a^2 - b^2\)[/tex] is:
[tex]\[
2a^2
\][/tex]
To consolidate:
- The sum of [tex]\((a^2 + b^2)\)[/tex] and [tex]\((a^2 - b^2)\)[/tex] simplifies to [tex]\(2a^2\)[/tex].
Hence, summing [tex]\(a^2 + b^2\)[/tex] and [tex]\(a^2 - b^2\)[/tex] gives us [tex]\(2a^2\)[/tex].
