Question

(6) 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 rectangle =(2a²+3b²)m

breadth of the rectangle =(a²+b²)m

area of the rectangle =l×b

=(2a²+3b²)×(a²+b²)

=2a⁴+2a²b²+3a²b²+3b⁴

=2a⁴+5a²b²+3b⁴

side of the square =(a²-b²)

area of the square =s×s=(a²-b²)(a²-b²)

=a⁴-a²b²-a²b²+b⁴

remaining part of the farm=area of the rectangle-area of the square

=(2a⁴+5a²b²+3b⁴)-(a⁴-2a²b²+b⁴)

=2a⁴+/a²b²+3b⁴-a⁴+2a²b²-b⁴

=a⁴+7a²b²+2b⁴