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[tex]\huge\boxed{\bold{\underline{\underline{Question:}}}}[/tex]

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

Thanks in advance.

[tex]\bold{(4t-3)^{5}}[/tex]

Respuesta :

tanmayakumarp3

Answer:

[tex] {1024t}^{5} - 3840{t}^{4} + 5760{t}^{3} - 4320{t}^{2} + 1620t- 243[/tex]

Step-by-step explanation:

Question:-

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

As we know:-

As in Binomial theorem :-

  • [tex] {(x - y)}^{5} = {x}^{5} - 5 {x}^{4} y + 10 {x}^{3} {y}^{2} - 10 {x}^{2} {y}^{3} + 5x {y}^{4} - {y}^{5} [/tex]

Solution :-

[tex] = {(4t - 3)}^{5} [/tex]

  • Hence, on using the Binomial theorem,

[tex]= {(4t)}^{5} - 5 {(4t)}^{4} (3)+ 10 {(4t)}^{3} {(3)}^{2} - 10 {(4t)}^{2} {(3)}^{3} + 5(4t) {(3)}^{4} - {(3)}^{5} [/tex]

  • On formatting

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

  • On further formatting.

[tex]= {1024t}^{5} - 3840{t}^{4} + 5760{t}^{3} - 4320{t}^{2} + 1620t- 243[/tex]

Hence, the required answer is :-

[tex]{1024t}^{5} - 3840{t}^{4} + 5760{t}^{3} - 4320{t}^{2} + 1620t- 243[/tex]

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