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A rectangle is formed by sides \( (x+2y) \) and \( (x-2y) \). Which expression does its area equal?एक आयत की भुजाएँ \( (x+2y) \) और \( (x-2y) \) हैं। उसका क्षेत्रफल कौन-सा व्यंजक होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2-4y^2\)\(x^2-4y^2\)
Area of the rectangle is the product of its side lengths:
\[ (x+2y)(x-2y). \]
This is a difference of squares: \( (x)^2-(2y)^2 \). So
\[ (x+2y)(x-2y)=x^2-(2y)^2=x^2-4y^2. \]
Hence option C.आयत का क्षेत्रफल भुजाओं के गुणनफल के बराबर होता है:
\[ (x+2y)(x-2y). \]
यह वर्गों का अंतर (difference of squares) है: \( x^2-(2y)^2 \)। इसलिए
\[ (x+2y)(x-2y)=x^2-(2y)^2=x^2-4y^2. \]
अतः सही विकल्प C है।
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