Question:
Write the general term in the expansion of $\left(x^{2}-y x\right)^{12}, x \neq 0$
Solution:
It is known that the general term $T_{r+1}$ \{which is the $(r+1)^{\text {th }}$ term $\}$ in the binomial expansion of $(a+b)^{n}$ is given by $T_{r+1}={ }^{n} C_{r} a^{n-r} b^{r}$.
Thus, the general term in the expansion of $\left(x^{2}-y x\right)^{12}$ is
$\mathrm{T}_{\mathrm{r}+1}={ }^{12} \mathrm{C}_{\mathrm{r}}\left(\mathrm{x}^{2}\right)^{12-\mathrm{t}}(-\mathrm{yx})^{\mathrm{r}}=(-1)^{\mathrm{r}}{ }^{12} \mathrm{C}_{\mathrm{r}} \cdot \mathrm{x}^{24-2 \mathrm{r}} \cdot \mathrm{y}^{\mathrm{r}} \cdot \mathrm{x}^{\mathrm{r}}=(-1)^{\mathrm{r}}{ }^{12} \mathrm{C}_{\mathrm{r}} \cdot \mathrm{x}^{24-\mathrm{r}} \cdot \mathrm{y}^{\mathrm{r}}$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
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- Chemical Effects of Electric Current,
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