Question:
Tick (✓) the correct answer:
(a + 1)(a − 1)(a2 + 1) = ?
(a) (a4 − 2a2 − 1)
(b) (a4 − a2 − 1)
(c) (a4 − 1)
(d) (a4 + 1)
Solution:
(c) $\left(a^{4}-1\right)$
$(i)(a+1)(a-1)\left(a^{2}+1\right)$
$\Rightarrow\left((a)^{2}-(1)^{2}\right)\left(a^{2}+1\right)$ [according to the formula $a^{2}-b^{2}=(a+b)(a-b)$ ]
$\Rightarrow\left(a^{2}-1\right)\left(a^{2}+1\right)$
$\Rightarrow\left(a^{2}\right)^{2}-\left(1^{2}\right)^{2}$ [according to the formula $a^{2}-b^{2}=(a+b)(a-b)$ ]
$\Rightarrow a^{4}-1$