What is the formula for a2+b2?
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.