Which one among the following is indicated by the following figure ?
(Figure shows a square divided into four smaller rectangles. Top left is a x a, top right is a x b, bottom left is b x a, bottom right is b x b)
[amp_mcq option1=”a + ab + ab + b² = a/(1-b) for b < 1" option2="a³ > b³ ⇒ a > b” option3=”(a + b)² = a² + 2ab + b²” option4=”a > b ⇒ -a < -b" correct="option3"]
This question was previously asked in
UPSC CAPF – 2014
The figure shows a large square with side length (a + b). The area of this large square is (a + b) * (a + b) = (a + b)². This square is divided into four smaller rectangles with areas a*a (a²), a*b (ab), b*a (ab), and b*b (b²). The total area of the large square is also the sum of the areas of the four smaller rectangles: a² + ab + ab + b² = a² + 2ab + b². Therefore, the figure visually represents the algebraic identity (a + b)² = a² + 2ab + b².
The figure provides a geometric proof or illustration of the expansion of the binomial (a+b)².