taking a,b,c as positive integers,verify the following whether they are identities or not? (a-b)^2=a^2-2ab+b^2 ,(a+b)(a-b)=a^2-b^2
Answers
Step-by-step explanation:
a – b)2 ≡ a2 - 2ab + b2
Consider a square with side a.i.e.a = 5
The square is divided into 4 regions.
It consists of 2 squares with sides a-b and b respectively and 2 rectangles with length and breadth as ‘a-b’ and ‘b’ respectively.
Here a = 5 and b = 2.Therefore the 2 squares consist of sides ‘5-2’ and ‘2’ respectively and 2 rectangles with length and breadth as ‘5-2’ and ‘2’ respectively.
Now area of figure I = Area of whole square with side ‘a’ i.e.5 units-Area of figure II
-Area of figure III –Area of figure IV
L.H.S of area of figure I = (5-2)(5-2) = 3(3) = 9 units
R.H.S = Area of whole square with side 5 units-Area of figure II with 2,(5-2)units
-Area of figure III with 2,(5-2) units –Area of figure IV with 2,2 units = 25-(2×3)-
( 2×3)-22 = 25-6-6-4 = 9 units
L.H.S = R.H.S
Step-by-step explanation:
(a-b)^2=(a+b)(a-b)
=(a^2)-ab×ba +(b^2)
=a^2-2ab+b^2
(a-b)(a+b)=a^2-ab×-ab-b^2
=a^2-b^2