Geometrically explain the polynomial: (2x−3)2=4x2+32−12x
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Solution
Step 1: Draw a square ACDF with AC=2x. Step 2: Cut AB=3 so that BC=(2x−3). Step 3: Complete the squares and rectangle as shown in the diagram. Step 4: Area of yellow square IDEO= Area of square ACDF− Area of rectangle GOFE− Area of rectangle BCIO− Area of red square ABOG Therefore, (2x−3)2=(2x)2−3(2x−3)−3(2x−3)−(3)2 =4x2−6x+32−6x+32−32 =4x2+32−12x Hence, geometrically we proved the identity (2x−3)2=4x2+32−12x.