State whether the statement is True or False:
$(4 x^{2} - 5 y^{2}) (4 x^{2} + 5 y^{2})$ is equal to $16 x^{4} - 25 y^{4}$ .

True

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False

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Solution

The correct option is A True
Given, $(4 x^{2} - 5 y^{2}) (4 x^{2} + 5 y^{2})$ .

We know, $(a + b) (a - b)$ $= (a^{2} - b^{2})$ .

Multiply by using direct method, we get,
$(4 x^{2} - 5 y^{2}) (4 x^{2} + 5 y^{2})$ $= (4 x^{2})^{2} - (5 y^{2})^{2}$
$= 16 x^{4} - 25 y^{4}$ .

Hence, the statement is true.
Therefore, option $A$ is correct.

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1

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