If a square model is divided according to side lengths a and b and contains one square of area a², one square of area b², and two equal rectangles each of area ab, which algebraic identity does it represent?
A. \((a+b)^2=a^2+2ab+b^2\)
पूरे वर्ग की भुजा \(a+b\) है, इसलिए उसका क्षेत्रफल \((a+b)^2\) होगा। भागों का योग \(a^2+ab+ab+b^2\) है, अर्थात \(a^2+2ab+b^2\)। परीक्षा में दो \(ab\) आयतों को अवश्य गिनें। / The large square has side \(a+b\), so its area is \((a+b)^2\). Adding its parts gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option B would require subtraction, not two positive \(ab\) rectangles. Exam tip: count both rectangles.
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Correct Answer: A. \((a+b)^2=a^2+2ab+b^2\). Explanation: पूरे वर्ग की भुजा \(a+b\) है, इसलिए उसका क्षेत्रफल \((a+b)^2\) होगा। भागों का योग \(a^2+ab+ab+b^2\) है, अर्थात \(a^2+2ab+b^2\)। परीक्षा में दो \(ab\) आयतों को अवश्य गिनें। / The large square has side \(a+b\), so its area is \((a+b)^2\). Adding its parts gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option B would require subtraction, not two positive \(ab\) rectangles. Exam tip: count both rectangles.
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