What is the formula of x^2 + y^2?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The formula of x2 + y2 is (x + y)2 – 2xy or (x – y)2 + 2xy

To write the formula for x2 + y2

From (x + y)2 = x2 + y2 + 2xy

x2 + y2 = (x + y)2 – 2xy

Also from (x – y)2 = x2 + y2 – 2xy

x2 + y2 = (x – y)2 + 2xy

Algebraic Identities

Algebraic identities are the equations in algebra that are true regardless of the value of each of their variables. Mathematical equations with numbers, variables, and mathematical operators are known as algebraic identities and expressions (subtraction, division, addition, multiplication, etc.)

Numerous areas of mathematics, including geometry, algebra, trigonometry, etc., use algebraic identities. These are mainly employed to identify the polynomials’ factors. A deeper comprehension of algebraic identities helps to improve one’s ability to answer sum problems quickly. The factorization of polynomials is one of the most significant uses for algebraic identities.

An equation is said to be an identity if it is true regardless of the value of each of the variables. The equations that have the left side of the equation equaling the right side of the equation exactly for all possible values of the variable are known as algebraic identities.

Example: Consider the linear equation ax + b = 0

When x = -b/a, the left and right sides of the equations above are identical.

As a result, it is an equation rather than identity.

Therefore, the formula is (x + y)2 – 2xy or (x – y)2 + 2xy

Summary:-

What is the formula of x^2 + y^2?

The formula of x2 + y2 is (x + y)2 – 2xy or (x – y)2 + 2xy. The algebraic equations which are valid for all values of variables in them are called algebraic identities.

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