There is a rectangular farm with length( a²+b²)m and breadth(a²-b²) . Find area of the farm.
Answers
Answer:
The area of the remaining part of the farm :
\begin{gathered}({a}^{4} + 7 {a}^{2} {b}^{2} + 2 {b}^{4}) \: m^2 \\ \end{gathered}
(a
4
+7a
2
b
2
+2b
4
)m
2
Step-by-step explanation:
To form algebraic expression of the given condition; There is a rectangular farm with
length l= (2a²+3b²) metre and
breadth b= (a²+b²) metre.
Area of Rectangular farm: l × b
\begin{gathered}(2 {a}^{2} + 3 {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \\ \\ = > 2 {a}^{4} + 2 {a}^{2} {b}^{2} + 3 {b}^{2} {a}^{2} + 3 {b}^{4} \\ \\ = (2 {a}^{4} + 5 {a}^{2} {b}^{2} + 3 {b}^{4})\:m^2 \\ \\ \\ \end{gathered}
(2a
2
+3b
2
)×(a
2
+b
2
)
=>2a
4
+2a
2
b
2
+3b
2
a
2
+3b
4
=(2a
4
+5a
2
b
2
+3b
4
)m
2
ATQ The farmer used a square shaped plot of the farm to build a house. The side of the plot was (a²-b²) metre.
Area of square plot= side × side
\begin{gathered}( {a}^{2} - {b}^{2} ) \times ( {a}^{2} - {b}^{2} ) \\ \\ = {a}^{4} - {a}^{2} {b}^{2} - {b}^{2} {a}^{2} + {b}^{4} \\ \\ = > ( {a}^{4} - 2{a}^{2} {b}^{2} + {b}^{4}) \:\: m^2\\ \\ \end{gathered}
(a
2
−b
2
)×(a
2
−b
2
)
=a
4
−a
2
b
2
−b
2
a
2
+b
4
=>(a
4
−2a
2
b
2
+b
4
)m
2
Area of remaining part of the farm:
Area of rectangular farm- Area of square plot
\begin{gathered} = > 2 {a}^{4} + 5 {a}^{2} {b}^{2} + 3 {b}^{4} - ( {a}^{4} - 2{a}^{2} {b}^{2} + {b}^{4}) \\ \\ = > 2 {a}^{4} + 5 {a}^{2} {b}^{2} + 3 {b}^{4} - {a}^{4} + 2{a}^{2} {b}^{2} - {b}^{4}) \\ \\ = > 2 {a}^{4} - {a}^{4} + 5 {a}^{2} {b}^{2} + 2 {a}^{2} {b}^{2} + 3{b}^{4} - {b}^{4} \\ \\ = > ({a}^{4} + 7 {a}^{2} {b}^{2} + 2 {b}^{4}) \: \: m^2\\ \\ \end{gathered}
=>2a
4
+5a
2
b
2
+3b
4
−(a
4
−2a
2
b
2
+b
4
)
=>2a
4
+5a
2
b
2
+3b
4
−a
4
+2a
2
b
2
−b
4
)
=>2a
4
−a
4
+5a
2
b
2
+2a
2
b
2
+3b
4
−b
4
=>(a
4
+7a
2
b
2
+2b
4
)m
2
Step-by-step explanation:
army