Question

(6) Write down the information in the form of algebraic expression and simplify.
There is a rectangular farm with length (2a + 3b) metre and breadth (a + b) metre.
The farmer used a square shaped plot of the farm to build a house. The side of the
plot was (a - b) metre. What is the area of the remaining part of the farm ?
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Answer 1

Answer:

Area of the remaining part=Area of rectangular farm -Area of squaee shaped plot

step-1: If length=2a+3b

breadth=a+b

then. area=l*b

=(2a+3b)(a+b)

=2a2+2ab+3ab+3b2

=2a2+5ab+3b2

step-2:If side=a-b

area of square=side*side

=(a-b)(a-b)

=a2-2ab+b2

Area of the remaining part=(2a2+5ab+3b2)-(a2-2ab+b2)

=2a2+5ab+3b2-a2+2ab-b2

=2a2-a2+5ab+2ab+3b2-b2

=a2+7ab+2b2