1. Algebraic Identities

2. Let us consider (x + a) (x + b) (x + a) (x + b) = (x + a) (x + b)
General identity
Let us consider (x + a) (x + b)
(x + a) (x + b) = (x + a) (x + b)
= x(x + b) + a(x + b)
= x 2 + bx +ax + ab
= x2 + (a+b)x + ab
Thus, (x + a) (x + b) = x2 + (a+b)x + ab x x x x x x

3. Recap (a + b)2 = (a + b) (a + b) = a2 + 2ab + b2
(x + a) (x + b) = x2 + (a + b)x + ab

4. Example 1:- Find the value of (3m + 5) (3m + 5) using suitable identity
Solution:
The above algebraic expression is same as following identity
(a + b)2 = (a + b) (a + b) = a2 + 2ab + b2 Where a = 3m and b = 5
a2 + 2ab + b2
=(3m)2 + 2 x 3m x (After substituting value of a and b)
=9m2 + 30m (Ans)

5. Example 2:- Find the value of (2x - 3) (2x - 3) using suitable identity
Solution:
The above algebraic expression is same as following identity
(a - b)2 = (a - b)(a - b) = a2 - 2ab + b2 Where a = 2x and b = 3
a2 - 2ab + b2
=(2x)2 -2 x 2x x (After substituting value of a and b)
=4x2 - 12x (Ans)

6. Example 3:- Find the value of (2l – 3m) (2l + 3m) using suitable identity
Solution:
The above algebraic expression is same as following identity
(a + b) (a - b) = a2- b2 Where a = 2l and b = 3m
a2- b2
=(2l)2 – (3m)2 (After substituting value of a and b)
= 4l2 -9m2 (Ans)

7. Example 4:- Find the value of (5m + 3) (5m + 4) using suitable identity
Solution:
The above algebraic expression is same as following identity
(x + a) (x + b) = x2 + (a + b)x + ab Where x= 5m , a=3 and b= 4
x2 + (a + b)x + ab
= (5m)2 + ( 3 + 4) x 5m + 3x4 (After substituting value of x, a and b)
= 25m x 5m + 12
= 25m m (Ans)

8. Try these Using identity solve (2m + 3) (2m + 3) (3x – 5) (3x – 5)
(2y + 7) (2y - 7)
(8x + 5) (8x + 2)