1. Algebraic Identities intro

2. Algebraic Identities
Let us learn three important Algebraic Identities which are very
useful in solving many problems.
We obtain these Identities by multiplying a binomial by
another binomial.

3. Identity 1 Let us consider (a + b)2 (a + b)2 = (a + b) (a + b)
= a(a+b) + b(a+b)
= a2+ab + ab + b2
= a2+2ab+b2
Thus, (a + b)2 = a2+2ab+b2 x x x x x x

4. Identity 2 Let us consider (a - b)2 (a - b)2 = (a - b) (a - b)
= a(a - b) - b(a - b)
= a2 -ab -ab + b2
= a2-2ab+b2
Thus, (a - b)2 = a2- 2ab+b2 x x x x x x

5. Let us consider (a + b) (a - b) (a + b) (a - b) = (a + b) (a - b)
Identity 3
Let us consider (a + b) (a - b)
(a + b) (a - b) = (a + b) (a - b)
= a(a - b) + b(a - b)
= a2 -ab +ab - b2
= a2- b2
Thus, (a + b) (a - b) = a2-b2 x x x x x x

6. Recap (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2
(a + b) (a - b) = a2 - b2

7. Example 1:- Find the value of (x + 3)2 using suitable identity
Solution:
The above algebraic expression is same as following identity
(a + b)2 = a2 + 2ab + b2 Where a = x and b = 3
a2 + 2ab + b2
=x2 + 2 x x x (After substituting value of a and b)
=x2 + 6x (Ans)

8. Example 2:- Find the value of (y - 5)2 using suitable identity
Solution:
The above algebraic expression is same as following identity
(a - b)2 = a2 - 2ab + b2 Where a = y and b = 5
a2 - 2ab + b2
=y2 - 2 x y x (After substituting value of a and b)
=y y (Ans)

9. Example 3:- Find the value of (p – 5) (p + 5) using suitable identity
Solution:
The above algebraic expression is same as following identity
(a + b) (a - b) = a2- b2 Where a = p and b = 5
a2- b2
=p2 – 52 (After substituting value of a and b)
= p (Ans)

10. Try these
Using identity solve
(p + 4)2
(x - 7)2
(b + 4) (b - 4)