The formula for a²+b² is a fundamental expression in algebra. It represents the sum of the squares of two variables, a and b. In this article, we will delve into this formula, its significance, and how it simplifies mathematical expressions.

Answer: The formula for a²+b² is (a+b)²−2ab.

The formula for a² + b² can be derived using basic algebraic identities. The square of a binomial, (a+b)², is given by a²+b²+ 2ab. To express a²+b² in terms of (a+b)², we need to manipulate this identity.

Starting with (a+b)²= a²+b²+ 2ab, we can rearrange it to isolate a²+b². Subtract 2ab from both sides of the equation:

(a+b)²= a²+b²+ 2ab

Simplifying the right-hand side, we get:

(a+b)²−2ab = a²+b²

Thus, a²+b² can be expressed as:

a²+b² = (a +b)²−2ab

Hence, a²+b² can be expressed as (a+b)²−2ab.

This formula shows that the sum of the squares of two numbers, a and b is equal to the square of their sum minus twice their product. This derivation is a straightforward application of algebraic manipulation and the expansion of the square of a binomial.