Question

Find the value of
$(a + 1)(a - 1)( {a}^{2 } + 1)$
​

Answer 1

Answer:

${a}^{4} - 1$

Step-by-step explanation:

$(a - 1)(a + 1)( {a}^{2} + 1) \\ \\ = (a - 1)(a + 1) \: \: which \: \: is \: \: equal \: to \: \: {a}^{2} - {1}^{2} \\ \\ so \\ \\ = ( {a}^{2} - 1)( {a}^{2} + 1) \\ \\ again \: \: \: from \: \: equation \: \: of \: \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = {a}^{4} - {1}^{4} \\ \\ because \: in \: our \: case \: \: a = {a}^{2} \: \: and \: b = 1 \\ \\ final \: answer \: is \: {a}^{4} - 1$

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Answer 2

Answer:

(a²-1²)(a²+1)

a²(a²+1) - 1²(a²+1)

a²(a²+1) - 1(a²+1)

a^4 + a² -1a² -1

This is the answer