Answer the following: Expand (2x3-32x)4 - Mathematics and Statistics

प्रश्न

Answer the following:

Expand ${(\frac{2 x}{3} - \frac{3}{2 x})}^{4}$

योग

उत्तर

${(\frac{2 x}{3} - \frac{3}{2 x})}^{4} =^{4} C_{0} {(\frac{2 x}{3})}^{4} -^{4} C_{1} {(\frac{2 x}{3})}^{3} (\frac{3}{2 x}) +^{4} C_{2} {(\frac{2 x}{3})}^{2} {(\frac{3}{2 x})}^{2} -^{4} C_{3} (\frac{2 x}{3}) {(\frac{3}{2 x})}^{3} +^{4} C_{4} {(\frac{3}{2 x})}^{4}$

Now, ⁴C₀ = 1 = ⁴C₄

⁴C₁ = 4 = ⁴C₃

⁴C₂ = $\frac{4 \times 3}{1 \times 2}$ = 6

∴ ${(\frac{2 x}{3} - \frac{3}{2 x})}^{4} = 1 \times \frac{16 x^{4}}{81} - 4 \times \frac{8 x^{3}}{27} \times \frac{3}{2 x} + 6 \times \frac{4 x^{2}}{9} \times \frac{9}{4 x^{2}} - 4 \times \frac{2 x}{3} \times \frac{27}{8 x^{3}} + 1 \times \frac{81}{16 x^{4}}$

= $\frac{16 x^{4}}{81} - \frac{16 x^{2}}{9} + 6 - \frac{9}{x^{2}} + \frac{81}{16 x^{4}}$

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Binomial Theorem for Negative Index Or Fraction

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q II. (5)Q II. (4)Q II. (6)

अध्याय 4: Methods of Induction and Binomial Theorem - Miscellaneous Exercise 4.2 [पृष्ठ ८५]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board

अध्याय 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4.2 | Q II. (5) | पृष्ठ ८५

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