Question 80

In the following question, state whether the statement is True (T) or False (F):

The value of $(a + 1) (a - 1) (a^{2} + 1)$ is $a^{4} - 1$ .

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Solution

True

We have,
$(a + 1) (a - 1) (a^{2} + 1) = (a^{2} - 1) (a^{2} + 1)$
[Using the identity, $(a + b) (a - b) = a^{2} - b^{2}$ in first two factors]
$= (a^{2})^{2} - 1^{2}$
$= a^{4} - 1$

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