What is an Identity?

An identity is an equality which is true for every value of the variable.

(a + b)= a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

a2 – b2 = (a + b) (a – b)

(x + a) (x + b) = x2 + (a + b)x + ab

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Example

(4x – 3y)2

= (4x)2 – 2(4x) (3y) + (3y)

= 16x2 – 24xy + 9y2

Example

Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the value of 501 × 502

Solution:

 501 × 502

= (500 + 1) × (500 + 2)

 = 5002 + (1 + 2) × 500 + 1 × 2

= 250000 + 1500 + 2

= 251502  

Scroll to Top