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Alborosie
2 years ago
9

ula1" title="\huge\boxed{\bold{\underline{\underline{Question:}}}}" alt="\huge\boxed{\bold{\underline{\underline{Question:}}}}" align="absmiddle" class="latex-formula">
Hi! Can anyone please help me with my homework? I would be grateful. No spam.

Thanks in advance.

\bold{(4t-3)^{5}}
Mathematics
1 answer:
Ronch [10]2 years ago
6 0

Answer:

<h2> </h2><h2>{1024t}^{5}  - 3840{t}^{4} + 5760{t}^{3} - 4320{t}^{2}   + 1620t-  243</h2>

Step-by-step explanation:

<h3><em><u>Question</u></em><em><u>:</u></em><em><u>-</u></em></h3>
  • To find the Binomial theorem form of \bold{(4t-3)^{5}}
<h3><em><u>As</u></em><em><u> </u></em><em><u>we</u></em><em><u> </u></em><em><u>know</u></em><em><u>:</u></em><em><u>-</u></em></h3>

<em>As</em><em> </em><em>in</em><em> </em><em>Bin</em><em>omial</em><em> </em><em>theorem</em><em> </em><em>:</em><em>-</em>

  • {(x - y)}^{5}  =  {x}^{5}  - 5 {x}^{4} y + 10 {x}^{3}  {y}^{2}  - 10 {x}^{2}  {y}^{3}  + 5x {y}^{4}  -  {y}^{5}
<h3><em><u>Solution</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em></h3>

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

  • <em>Hence</em><em>,</em><em> </em><em>on</em><em> </em><em>using</em><em> </em><em>the</em><em> </em><em>Binomial</em><em> </em><em>theorem</em><em>,</em><em> </em>

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

  • <em>On</em><em> </em><em>formatting</em><em> </em>

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

  • <em>On</em><em> </em><em>further</em><em> </em><em>formatting</em><em>.</em><em> </em>

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

<em><u>Hence</u></em><em><u>,</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>required</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em>

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

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