Question

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

Answer 1

The area of the rectangular farm whose length and breadth are $2a^2+3b^2$ metre and $a^2+b^2$ respectively is $=(2a^2+3b^2)(a^2+b^2)$ metre${}^2$.

The area of the square plot whose side is of $a^2-b^2$ metre${}^2$.

Then the area of the remaining part of the farm $=(2a^2+3b^2)(a^2+b^2)-(a^2-b^2{)}^2=a^4+7a^2{b}^2+2b^4$ metre${}^2$.