Expand 2a- 3 b 5 by binomial theorem

The correct option is A [ 32a ^ 5 240a ^ 4 b + 720a ^ 3 b ^ 2 1080a ^ 2 b ^ 3 + 810a ^ b ^ 4 243 ^ b ^ 5 ] (2a 3b)^5 =(2a)^5+5(2a) ...

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Standard XII

Mathematics

Binomial Coefficients

Expand 2a- ...

Question

Expand ${(2 a - \frac{3}{b})}^{5}$ by binomial theorem

[{32 a}^{5} - \frac{{240 a}^{4}}{b} + \frac{{720 a}^{3}}{b^{2}} - \frac{{1080 a}^{2}}{b^{3}} + \frac{{810 a}}{b^{4}} - \frac{243}{b^{5}}]

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[{32 a}^{5} + \frac{{240 a}^{4}}{b} + \frac{{144 a}^{3}}{b^{2}} + \frac{{1080 a}^{2}}{b^{3}} + \frac{{810 a}}{b^{4}} + \frac{243}{b^{5}}]

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[{32 a}^{5} + \frac{{240 a}^{4}}{b} + \frac{{720 a}^{3}}{b^{2}} + \frac{{1080 a}^{2}}{b^{3}} + \frac{{810 a}}{b^{4}} + \frac{253}{b^{5}}]

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[{32 a}^{5} - \frac{{240 a}^{4}}{b} + \frac{{720 a}^{3}}{b^{2}} - \frac{{1080 a}^{2}}{b^{3}} + \frac{{810 a}}{b^{4}} - \frac{253}{b^{5}}]

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Solution

The correct option is A $[{32 a}^{5} - \frac{{240 a}^{4}}{b} + \frac{{720 a}^{3}}{b^{2}} - \frac{{1080 a}^{2}}{b^{3}} + \frac{{810 a}}{b^{4}} - \frac{243}{b^{5}}]$
${(2 a - \frac{3}{b})}^{5}$ $= {(2 a)}^{5} + 5 {(2 a)}^{4} {(\frac{3}{b})}^{1} + 10 {(2 a)}^{3} {(\frac{3}{b})}^{2} + 10 {(2 a)}^{2} {(\frac{3}{b})}^{3} + 5 {(2 a)}^{1} {(\frac{3}{b})}^{4} + {(\frac{3}{b})}^{5}$
$= 32 a^{5} - \frac{240 a^{4}}{b} + \frac{720 a^{3}}{b^{2}} - \frac{1080 a^{2}}{b^{3}} + \frac{810 a}{b^{4}} - \frac{243}{b^{5}}$

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