# Evaluate the Following Using Identities: 117 ☓ 83 - Mathematics

Evaluate the following using identities:

117 x 83

#### Solution

The given expression is  117 x 83

We have

(117 + 83)/2 = 200/2

= 100

So we can express 117 and 83 in the terms of 100 as

117 = 100 + 17

83 = 100 - 17

117 x 83 = (100 + 17)(100 - 17)

We shall use the identity (x - y)(x + y) = x^2 - y^2

Here

(x + y) = 100 + 17

(x - y) = 100 - 17

By applying in identity we get

(100 + 17)(100 - 17) = (100)^2 - (17)^2

= 10000 - 289

= 9711

Hence the value of 1117 x 83 is 9711

Concept: Algebraic Identities
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.1 | Q 2.4 | Page 7

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