Which of the following figure is true for the polynomial $4 x^{2} + 3^{2} - 12 x$ ?

figure 3

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figure 2

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figure 4

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figure 1

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Solution

The correct option is C figure 4
Area of yellow square $I D E O =$ Area of square $A C D F$ $-$ Area of rectangle $G O F E$ $-$ Area of rectangle $B C I O$ $-$ Area of red square $A B O G$
Therefore, $(2 x - 3)^{2} = (2 x)^{2} - 3 (2 x - 3) - 3 (2 x - 3) - (3)^{2}$
$=$ $4 x^{2} - 6 x + 3^{2} - 6 x + 3^{2} - 3^{2}$
$=$ $4 x^{2} + 3^{2} - 12 x$
Hence, the figure 3 is the solution for the given geometrical representation $(2 x - 3)^{2} = 4 x^{2} + 3^{2} - 12 x$

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