Algebraic Identities

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

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

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 5 + 52 (After substituting value of a and b) =9m2 + 30m + 25 (Ans)

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 3 + 32 (After substituting value of a and b) =4x2 - 12x + 9 (Ans)

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)

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) = 25m2 + 7 x 5m + 12 = 25m2 + 35m + 12 (Ans)

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