To simplify [tex]\((a+b)^2 + (a-b)^2\)[/tex], we can use basic algebraic identities and steps.
1. Expand each part of the expression using the formula for the square of a binomial:
[tex]\[
(a+b)^2 = a^2 + 2ab + b^2
\][/tex]
[tex]\[
(a-b)^2 = a^2 - 2ab + b^2
\][/tex]
2. Add the expanded forms together:
[tex]\[
(a^2 + 2ab + b^2) + (a^2 - 2ab + b^2)
\][/tex]
3. Combine like terms:
- [tex]\(a^2\)[/tex] terms: [tex]\(a^2 + a^2 = 2a^2\)[/tex]
- [tex]\(2ab\)[/tex] terms: [tex]\(2ab - 2ab = 0\)[/tex]
- [tex]\(b^2\)[/tex] terms: [tex]\(b^2 + b^2 = 2b^2\)[/tex]
4. Simplify the expression:
[tex]\[
2a^2 + 0 + 2b^2 = 2a^2 + 2b^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
(a+b)^2 + (a-b)^2 = 2a^2 + 2b^2
\][/tex]
