Multiplication Identities - STD 9 - Page 82.1 EM

Two Numbers - Product and Difference

Using (x + y)(u - v) type identity

Problem

The product of two numbers is 713 and their difference is 8.

(i) Product of larger increased by 1 and smaller decreased by 1
(ii) Product of larger decreased by 1 and smaller increased by 1

Product

713

Difference

8

Step-by-Step Solution (Using Identities)

Step 1: Let the numbers be x (larger) and y (smaller)

xy = 713
x - y = 8

Step 2: Find (x + 1)(y - 1)

(x + 1)(y - 1) = xy - x + y - 1
= xy - (x - y) - 1
= 713 - 8 - 1 = 704

Step 3: Find (x - 1)(y + 1)

(x - 1)(y + 1) = xy + x - y - 1
= xy + (x - y) - 1
= 713 + 8 - 1 = 720

(i) Larger +1 and Smaller -1

704

(ii) Larger -1 and Smaller +1

720