Let's simplify the expression [tex]\((a+b)^2 - 2ab\)[/tex]:
1. Expand the square term [tex]\((a+b)^2\)[/tex]:
Using the binomial theorem:
[tex]\[
(a+b)^2 = a^2 + 2ab + b^2
\][/tex]
2. Rewrite the given expression with the expanded form:
The original expression is:
[tex]\[
(a+b)^2 - 2ab
\][/tex]
Substitute the expanded form:
[tex]\[
a^2 + 2ab + b^2 - 2ab
\][/tex]
3. Combine like terms:
Notice that [tex]\(2ab\)[/tex] and [tex]\(-2ab\)[/tex] are like terms and they cancel each other out:
[tex]\[
a^2 + 2ab + b^2 - 2ab = a^2 + (2ab - 2ab) + b^2 = a^2 + b^2
\][/tex]
4. Write the simplified expression:
The simplified form of [tex]\((a+b)^2 - 2ab\)[/tex] is:
[tex]\[
a^2 + b^2
\][/tex]
Therefore, the final simplified expression is [tex]\(a^2 + b^2\)[/tex].
