Question

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

There is a rectangular farm with length (2a² + 3b²) meter and breadth (a² + b²) meter. the farmer used a square shaped plot of the farm to build a house. the side of the plot was (a² - b²) meter. what is the area of the remaining part of the farm ? ​

Answer 1

Answer:

I hope it will be help full for you

Answer 2

The Remaining area is

$(a^4+7a^2b^2+2b^4)$

Formula:

Area of Rectangle=Length×breadth

$\begin{gathered}Area \ of \ rectangle =(2a^2+3b^2)(a^2+b^2)\\=2a^4+2a^2b^2+3a^2b^2+3b^4\\=(2a^4+5a^2b^2+3b^4)m^2\end{gathered}$

Area of Square=Length×Length

$\begin{gathered}Area \ of \ square =(a^2-b^2)(a^2-b^2)\\=a^4-a^2b^2-a^2b^2+b^4\\=(a^4-2a^2b^2+b^4)m^2\end{gathered} </p><p>$

Remaining area= Area of Rectangle-Area of Square

$\begin{gathered}=(2a^4+5a^2b^2+3b^4)-(a^4-2a^2b^2+b^4)\\=2a^4+5a^2b^2+3b^4-a^4+2a^2b^2-b^4\\=(a^4+7a^2b^2+2b^4)m^2\end{gathered}$