Question

(a+b) whole 4what will be the answer please let me know

Answer 1

hello users ....

solution:-
we know that
(a+b)² = a² + b² + 2ab

Here,
(a + b)∧4 = (a+b)² * (a+b)² 

= (a² + b² + 2ab)*(a² + b² + 2ab)

= [ a²(a² + b² + 2ab) + b²(a² + b² + 2ab) + 2ab(a² + b² + 2ab) ]

= [ a∧4 +a²b² + 2a³b + a²b² + b∧4 + 2ab³ + 2a³b + 2ab³ + 4a²b² ]

= [ a∧4 + b∧4 + (a²b² + a²b² + 4a²b²) + (2a³b + 2a³b) + (2ab³ + 2ab³) ]

= [ a∧4 + b∧4 + 6a²b² + 4a³b + 4ab³] Answer 

# hope it helps :)

Answer 2

Heya user,

[ a + b ]⁴ can be expanded using Binomial theorem as -->

[ a + b ]⁴ = 4C0 a⁴ + 4C1 a³b + 4C2 a²b² + 4C3 ab³ + 4C4 b⁴
=> [ a + b ]⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

Yep! ---> Binomial theorem can help expand any binomial [ a + b ]ⁿ.

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Other method --->
[ a + b ]² = a² + 2ab + b²
=> [ a + b ]² [ a + b ]² =
----------> a² [ a² + 2ab + b² ] + 2ab [ a² + 2ab + b² ] + b²[ a² + 2ab + b² ]
====== a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ <--- Desired result