**Evaluation of 53×55 using suitable identities**

To evaluate the expression 53×55, we can make use of suitable identities to simplify the calculation. One such identity that can be used in this case is the identity for squaring a binomial.

**The Identity for Squaring a Binomial:**
(a + b)^2 = a^2 + 2ab + b^2

In this case, we can treat 53 as (50 + 3) and 55 as (50 + 5) to take advantage of this identity. Let's break down the steps to evaluate 53×55 using this identity:

1. Express 53 as (50 + 3) and 55 as (50 + 5):
53 = 50 + 3
55 = 50 + 5

2. Apply the identity for squaring a binomial:
(50 + 3) × (50 + 5) = (50^2 + 2 × 50 × 3 + 3^2) × (50^2 + 2 × 50 × 5 + 5^2)

3. Simplify each term within the parentheses:
(50^2 + 2 × 50 × 3 + 3^2) = (2500 + 300 + 9)
(50^2 + 2 × 50 × 5 + 5^2) = (2500 + 500 + 25)

4. Multiply the simplified terms:
(2500 + 300 + 9) × (2500 + 500 + 25) = 2500 × 2500 + 2500 × 500 + 2500 × 25 + 300 × 2500 + 300 × 500 + 300 × 25 + 9 × 2500 + 9 × 500 + 9 × 25

5. Perform the multiplications and additions:
2500 × 2500 = 6,250,000
2500 × 500 = 1,250,000
2500 × 25 = 62,500
300 × 2500 = 750,000
300 × 500 = 150,000
300 × 25 = 7,500
9 × 2500 = 22,500
9 × 500 = 4,500
9 × 25 = 225

6. Add up all the results:
6,250,000 + 1,250,000 + 62,500 + 750,000 + 150,000 + 7,500 + 22,500 + 4,500 + 225 = 8,507,225

Hence, 53×55 is equal to 8,507,225.

53=50+3
55=50+5 ,
=(50+3) × (50+5)
[this expression looks like( x+a)(x+b) ]
(x+a)(x+b)= x^2 +(a+b)x