Find the polynomial identity used in the diagram.

(5 n + 6 m) (5 n - 6 m) = (n)^{2} - (6 m)^{2}

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(5 n + 6 m) (5 n - 6 m) = (5 n)^{2} - (6 m)^{2}

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(5 n + 6 m) (5 n + 6 m) = (5 n)^{2} - (6 m)^{2}

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(5 n + 6 m) (5 n - 6 m) = (5 n)^{2} + (6 m)^{2}

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Solution

The correct option is B $(5 n + 6 m) (5 n - 6 m) = (5 n)^{2} - (6 m)^{2}$
The given identity is $(5 n + 6 m) (5 n - 6 m) = (5 n)^{2} - (6 m)^{2}$
Area of full square $=$ area of pink rectangle $+$ area of blue rectangle.
i.e., $(5 n)^{2} - (6 m)^{2} = 5 n (5 n - 6 m) + 6 m (5 n - 6 m)$
$(5 n)^{2} - (6 m)^{2} = (5 n + 6 m) (5 n - 6 m)$
So, $(5 n + 6 m) (5 n - 6 m) = (5 n)^{2} - (6 m)^{2}$ is used in the diagram.

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