a2 + b2 is Equal to

By K Balaji|Updated : September 21st, 2022

a2 + b2 is equal to (a + b)² – 2ab. The formula has been derived from the equation (a + b)2 = a2 + 2ab + b2. The method to derive a2 + b2 formula is called factorisation wherein an algebraic expression is represented as the product of two or more expressions. To factorise an expression, it is written as a product of its factors which may be numbers, algebraic variables, or algebraic expressions.

On factorising the expression (a + b)2 = a2 + 2ab + b2 we can obtain the formula of a2 + b2. The factorisation is done by using the distributive law property.

a2 + b2 formula is (a + b)² – 2ab or a2 + b2 = (a + b)² – 2ab

The derivation of the formula has been illustrated below:

  • We know that the a2+b2 formula has been derived from (a + b)2 = a2 + 2ab + b2.
  • Now, we will solve the above equation.
  • In this equation, (a + b)2 = a2 + 2ab + b2 we will place 2ab from right hand side to left and side.
  • Then the equation will be (a + b)2 - 2ab = a2 + b2.
  • Hence, a2 + b2 is equal to (a + b)² – 2ab.

Summary:

What is a2 + b2 Formula?

The formula of a2 + b2 is equal to (a + b)² – 2ab. The other identities related to a2 b2 formula are (a + b) (a – b) = a2 – b2, (a – b)2 = a2 – 2ab + b2, (x + a) (x + b) = x2 + (a + b) x + ab.

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