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Question

Geometrically explain the polynomial: (2x3)2=4x2+3212x

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Solution

Step 1: Draw a square ACDF with AC=2x.
Step 2: Cut AB=3 so that BC=(2x3).
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, (2x3)2=(2x)23(2x3)3(2x3)(3)2
= 4x26x+326x+3232
= 4x2+3212x
Hence, geometrically we proved the identity (2x3)2=4x2+3212x.
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