(a+1) (a-1) (a²+1) please solve this problem
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Answered by
1
Answer:
a⁴-1
Step-by-step explanation:
We have been given the expression:-
(a+1)(a-1)(a^{2}+1)(a+1)(a−1)(a
2
+1)
Using the identity a^{2} - b^{2}= (a+b)(a-b)a
2
−b
2
=(a+b)(a−b) :-
= (a^{2} - 1^2)(a^{2}+1)(a
2
−1
2
)(a
2
+1)
= (a^{2} - 1)(a^{2} + 1)(a
2
−1)(a
2
+1)
Again using the identity a^2 - b^2 = (a+b)(a-b)a
2
−b
2
=(a+b)(a−b) :-
= [(a^{2})^{2} - 1^{2}][(a
2
)
2
−1
2
]
= (a^{4} - 1)(a
4
−1)
So, it can be evaluated to (a^{4} - 1)(a
4
−1)
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