# Write Down the Information in the Form of Algebraic Expression and Simplify. - Algebra

Sum

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

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

#### Solution

Lenght of the rectangular farm = (2a2 + 3b2) m

Breadth of the rectangular farm = (a2 + b2) m

Side of the square plot = (a2 − b2) m

∴ Area of the remaining part of the farm

= Total area of the farm − Area of the square plot

= Lenght of the rectangular farm × Breadth of the rectangular farm − (Side of the square plot)2

= (2a2 + 3b2) × (a2 + b2) − (a2 − b2)2

= 2a2(a2 + b2) + 3b2(a2 + b2) − (a4 + b− 2a2b2)

= 2a+ 2a2b+ 3a2b2 + 3b4 − a4 − b+ 2a2b2

= 2a4 − a4 + 2a2b2  + 3a2b+ 2a2b+ 3b− b4

= (a4 + 7a2b+ 2b4) m2

Thus, the area of the remaining part of the farm is (a4 + 7a2b+ 2b4) m2.

Concept: Operations on Polynomials
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 3 Polynomials
Practice Set 3.2 | Q 6 | Page 43