Q6 of 84 Page 43

Write down the information in the form of algebraic expression and simplify.

There is a rectangular farm with length (2a2 + 3b2) meter and breadth (a2 + b2) meter. The farmer used a square shaped plot of the farm to build a house. The side of the plot was (a2 - b2) meter. What is the area of the remaining part of the farm?

Given:

Length of the farm, l = (2a2 + 3b2) m


Breadth of the farm, b = (a2 + b2) m


Side of the square plot, s = (a2 - b2) m


To find: Area of remaining farm


Explain:


Area of Remaining Farm = Area of Rectangle – Area of Square


Area of Rectangle = l × b


= (2a2 + 3b2) × (a2 + b2)


= 2a2.a2 + 2a2.b2 + 3b2.a2 + 3b2.b2


= 2a4 + 5a2b2 + 3b4


Area of Square = s × s


= (a2 - b2) × (a2 - b2)


= a2.a2 – a2.b2 – a2.b2 + b2.b2


= a4 – 2a2b2 + b4


Area of Remaining Part = (2a4 + 5a2b2 + 3b4) – (a4 – 2a2b2 + b4)


= 2a4 + 5a2b2 + 3b4 - a4 + 2a2b2 - b4


= a4 + 7a2b2 + 2b4


Therefore, the area of remaining portion is = a4 + 7a2b2 + 2b4


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