Algebraic Identities

Solved Examples


Ex 1: Use the identity: (a+b)2 = a2 + 2ab + b2


Q: Find the value of (6 + 4)2 using the identity.


Solution:
We know,


(a + b)2 = a2 + 2ab + b2


Here,



  • a = 6   b = 4 


(6+4)2 = 62 + 2(6)(4) + 42 = 36 + 48 + 16 = 100


Ans: 100


Ex 2 : Use the identity: (a − b)2 = a2 − 2ab + b2


Q. Find the value of (9 - 2)2 using the identity.


Solution:
We know,


(a−b)2 = a2 − 2ab + b2


Here,



  • a = 9,  b = 2


(9 − 2)2 = 92 − 2(9)(2) + 22 = 81 − 36 + 4 = 49


Ans: 49


Ex 3 : Use the identity: (a + b) (a − b) = a2 − b2


Q. Find the value of (12 + 5)(12 − 5) using the identity.


Solution:
We know,


(a + b)(a − b) = a2 − b2 


Here,



  • a = 12   b = 5


(12+5)(12−5) = 122 − 52 = 144 − 25 = 


Ans: 119