State whether the statement is True or False:
On evaluating $(a + 1) (a - 1) (a^{2} + 1)$ , the answer is $a^{4} - 1$ .

True

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False

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Solution

The correct option is A True
Given, $(a + 1) (a - 1) (a^{2} + 1)$ .

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

Multiply by using direct method, we get,
$(a + 1) (a - 1) (a^{2} + 1) = [a^{2} - 1^{2}] (a^{2} + 1)$
$= (a^{2} + 1) (a^{2} - 1)$
Now, by using formula $(a^{2} - b^{2}) = (a + b) (a - b)$ , we get,
$= ((a^{2})^{2} - (1)^{2})$
$= a^{4} - 1$ .

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

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(b) (a⁴ − a² − 1)
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(d) (a⁴ + 1)

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State whether the statement is True or False:On evaluating (a+1)(a−1)(a2+1), the answer is a4−1.

State whether the statement is True or False:
On evaluating $(a + 1) (a - 1) (a^{2} + 1)$ , the answer is $a^{4} - 1$ .