Question

Evaluate using a suitable identity :95 multiplied by 97

Answer 1

Concept

Given a number x that is subtracted by a and b and then multiplied, the product will be

(x-a)(x-b)=(x^2)-x (a+b)+ab

Given

95 is multiplied by 97

Find

we need to evaluate 95×97 using a suitable identity

Solution

We have,

95×97

here we can write 95 as (100-5)

and similarly 97 will become (100-3)

thus, the identity will be

95×97 = (100-5) (100-3)

now we can expand the terms using the identity (x-a)(x-b)=(x^2)-x (a+b)+ab,

here x = 100, a = 5 and b = 3

= 100^2 - 100 (5+3) + 3*5

= 10000 - 800 + 15

= 10015 - 800

= 9215

Thus the value of 95×97 is 9215

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