Question

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

There is a rectangular farm with length (2a² + 3b² ) metre and breadth (a² + b² ) metre.The farmer used a square shaped plot of the farm to build a house. The side of the plot was (a² – b²) metre.

What is the area of the remaining part of the farm?

Answer 1

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

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

Area of the farm = length x breadth = (2a² + 3b² ) x (a² + b² ) 

= 2a² (a² + b²) + 3b² (a² + b² )

= 2a² + 2a²b² + 3a²b² + 3b⁴ 

= (2a⁴  + 5a²b² + 3b⁴ ) sq. m … (i) 

The farmer used a square shaped plot of the farm to build a house. 

Side of the square shaped plot = (a² – b² ) m 

∴ Area of the plot = (side)² 

= (a² – b² )²

= (a⁴ – 2a²b² + b⁴ ) sq m… .(ii) 

∴ Area of the remaining farm = Area of the farm – Area of the plot 

= (2a⁴ + 5a²b² + 3b⁴) – (a⁴ – 2a²b² + b⁴ ) … [From (i) and (ii)] 

= 2a⁴ + 5a²b² + 3b⁴ – a⁴+ 2a²b² – b⁴ 

= 2a⁴ – a⁴ + 5a²b² + 2a²b² + 3b⁴– b⁴ 

= a⁴+ 7a²b² + 2b⁴ 

∴ The area of the remaining farm is (a⁴ + 7a²b² + 2b⁴ ) sq. m.