(a+1)(a-1)(a2+1) Question
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Answer:
a⁴ - 1
Step-by-step explanation:
Given---> ( a + 1 ) ( a - 1 ) ( a² + 1 )
To find ---> Value of given expression
Solution----> We have an identity,
x² - y² = ( x + y ) ( x - y )
Now returning to original problem
( a + 1 ) ( a - 1 ) ( a² + 1 )
= { ( a + 1 ) ( a - 1 ) } ( a² + 1 )
Applying above property , we get
= { ( a )² - ( 1 )² } ( a² + 1 )
= ( a² - 1 ) ( a² + 1 )
Applying above property again , we get
= ( a² )² - ( 1 )²
= a⁴ - 1
Additional information--->
(1) ( a + b )² = a² + b² + 2ab
(2) ( a - b )² = a² + b² - 2ab
(3) ( a + b )³ = a³ + b³ + 3ab ( a + b )
(4) ( a - b )³ = a³ - b³ - 3ab ( a - b )
(5) a³ + b³ = ( a + b ) ( a² + b² - ab )
(6) a³ - b³ = ( a - b ) ( a² + b² + ab )
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a4-1
#answerwithquality #bal
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