Multiplication Identities - (x+y)(u+v) = xu+xv+yu+yv - STD 9 - EM

(x + y)(u + v) Expansion

Visual proof of the distributive property

Visual Representation

xv

yv

xu

yu

u + v

x + y

v

u

x

y

x = 3

y = 2

u = 4

v = 5

Step-by-Step Explanation

1

The big rectangle has width = (x + y) and height = (u + v).

2

Draw a vertical line at distance x from left and a horizontal line at distance u from bottom.

3

This divides the big rectangle into 4 smaller rectangles.

4

Area of each small rectangle = length × breadth.

Total Area = Area of big rectangle
= (x + y) × (u + v)

Also = xv + yv + xu + yu

(x + y)(u + v) = xu + xv + yu + yv

Live Calculation

xv

15

yv

10

xu

12

yu

8

Total Area

45

Both methods give the same result ✓