
a.
The regions representing a2−b2 .
a.

Answer to Problem 46E
Required figures and results are shown below.
Explanation of Solution
Given Information: Figure shows a large square with area a2 and a smaller square with area b2.
Calculation:
a2−b2= Area of larger square-Area of smaller square
zuyx
The area labeled by x,u,z (excluding y ) shows the region a2−b2 .
zux zux
Now, if the region x is shifted to the right of region u , then the new region is:
Clearly, area of this region is (a+b)(a−b) .
Thus, a2−b2=(a+b)(a−b)
b.
Use of figure to show (a−b)2=a2−2ab+b2.
b.

Answer to Problem 46E
Required figures and results are shown below.
Explanation of Solution
Given Information:Figure shows a large square with area a2 and a smaller square with area b2.
Calculation:
(a−b)2 =Area of region u
a2−2ab+b2=a2−ab−ab+b2
=Area of region (u+x+y+z) -Area of region (x+y) -Area of region (y+z) +Area of region y
=Area of region u
Hence proved.
Chapter 7 Solutions
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