Select a suitable identity and state whether the given equation is true or false :
$(a x^{2} + b y^{2}) (a x^{2} - b y^{2})$ is $a^{2} x^{4} + 2 a b x^{2} y^{2} + b^{2} y^{4}$

True

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False

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Solution

The correct option is B False
We multiply the given expression $(a x^{2} + b y^{2}) (a x^{2} - b y^{2})$ as shown below:

$(a x^{2} + b y^{2}) (a x^{2} - b y^{2}) = (a x^{2})^{2} - (b y^{2})^{2} (∵ s^{2} - t^{2} = (s + t) (s - t)) = a^{2} x^{4} - b^{2} y^{4}$

Hence, $(a x^{2} + b y^{2}) (a x^{2} - b y^{2}) = a^{2} x^{4} - b^{2} y^{4}$ .

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