Question

there is rectangle 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

Answer:

The Remaining area is $(a^4+7a^2b^2+2b^4)m^2$.

Step-by-step explanation:

Formula:      

                Area of Rectangle=Length×breadth

$Area \ of \ rectangle =(2a^2+3b^2)(a^2+b^2)\\=2a^4+2a^2b^2+3a^2b^2+3b^4\\=(2a^4+5a^2b^2+3b^4)m^2$

                Area of Square=Length×Length

$Area \ of \ square =(a^2-b^2)(a^2-b^2)\\=a^4-a^2b^2-a^2b^2+b^4\\=(a^4-2a^2b^2+b^4)m^2$

                 Remaining area= Area of Rectangle-Area of Square

$=(2a^4+5a^2b^2+3b^4)-(a^4-2a^2b^2+b^4)\\=2a^4+5a^2b^2+3b^4-a^4+2a^2b^2-b^4\\=(a^4+7a^2b^2+2b^4)m^2$

Hope You Find it Helpful  :)