7.2 Binomial Theorem for Positive Integral Index

Ask AI

Solved Examples

Using Binomial Theorem with n=4,a=x2,b=3xn=4, a=x^2, b=\frac{3}{x}: =4C0(x2)4+4C1(x2)3(3x)+4C2(x2)2(3x)2+4C3(x2)(3x)3+4C4(3x)4= ^4C_0 (x^2)^4 + ^4C_1 (x^2)^3 (\frac{3}{x}) + ^4C_2 (x^2)^2 (\frac{3}{x})^2 + ^4C_3 (x^2) (\frac{3}{x})^3 + ^4C_4 (\frac{3}{x})^4

Simplify terms:

  1. 1⋅x81 \cdot x^8
  2. 4⋅x6⋅3x=12x54 \cdot x^6 \cdot \frac{3}{x} = 12x^5
  3. 6⋅x4⋅9x2=54x26 \cdot x^4 \cdot \frac{9}{x^2} = 54x^2
  4. 4⋅x2⋅27x3=108x4 \cdot x^2 \cdot \frac{27}{x^3} = \frac{108}{x}
  5. 1⋅81x4=81x41 \cdot \frac{81}{x^4} = \frac{81}{x^4}

Result: x8+12x5+54x2+108x+81x4x^8 + 12x^5 + 54x^2 + \frac{108}{x} + \frac{81}{x^4}.

Interactive Solver