Question

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

There is a rectangular farm with length $\left(2a^2+3b^2\right)$ 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 ?

Answer 1

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 + b⁴ − 2a²b²)

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

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

= (a⁴ + 7a²b² + 2b⁴) m²

Thus, the area of the remaining part of the farm is (a⁴ + 7a²b² + 2b⁴) m².