Question

`\huge\boxed{\bold{\underline{\underline{Question:}}}}`

Hi! Can anyone please help me with my homework? I would be grateful. No spam.

Thanks in advance.


`\bold{(4t-3)^(5)}`

Answer 1

`{1024t}^(5) - 3840{t}^(4) + 5760{t}^(3) - 4320{t}^(2) + 1620t- 243`

Explanation:

Question:-

• To find the Binomial theorem form of
  `\bold{(4t-3)^(5)}`

As we know:-

As in Binomial theorem :-

• 
  `{(x - y)}^(5) = {x}^(5) - 5 {x}^(4) y + 10 {x}^(3) {y}^(2) - 10 {x}^(2) {y}^(3) + 5x {y}^(4) - {y}^(5)`

Solution :-

`= {(4t - 3)}^(5)`

• Hence, on using the Binomial theorem,

`= {(4t)}^(5) - 5 {(4t)}^(4) (3)+ 10 {(4t)}^(3) {(3)}^(2) - 10 {(4t)}^(2) {(3)}^(3) + 5(4t) {(3)}^(4) - {(3)}^(5)`

• On formatting

`= {1024t}^(5) - 5 ({256t}^(4) )(3)+ 10 ({64t}^(3) ) (9 ) - 10 ({16t}^(2) )(27) + 5(4t) (81) - 243`

• On further formatting.

`= {1024t}^(5) - 3840{t}^(4) + 5760{t}^(3) - 4320{t}^(2) + 1620t- 243`

Hence, the required answer is :-

`{1024t}^(5) - 3840{t}^(4) + 5760{t}^(3) - 4320{t}^(2) + 1620t- 243`