write down the information in the form of algebraic expressions 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?
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Answer:
Remaining area of rectangular farm = a^4 + 7a²b² + 2b^4
Step-by-step explanation:
lenght = 2a² + 3b², breadth = a² + b²
Area of rectangular farm = lenght x breadth
Area of rectangular farm = (2a² + 3b²)(a² + b²)
= 2a^4 + 5a²b² + 3b^4 ..... eqn 1
Area of plot =(a² - b²)(a² - b²)
= a^4 - 2a²b² + b^4 ...... eqn 2
Area of farm remaining = eqn 1 - eqn 2
= (2a^4 + 5a²b² + 3b^4) - (a^4 - 2a²b² + b^4)
= 2a^4 + 5a²b² + 3b^4 - a^4 + 2a²b² - b^4
= a^4 + 7a²b² + 2b^4
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