Question:
Find the value
$\frac{1}{27} x^{3}-y^{3}+125 z^{3}+5 x y z$
Solution:
$=(x / 3)^{3}+(-y)^{3}+(5 z)^{3}-3 \times x / 3(-y)(5 z)$
$=(x / 3+(-y)+5 z)\left((x / 3)^{2}+(-y)^{2}+(5 z)^{2}-x / 3(-y)-(-y) 5 z-5 z(x / 3)\right)$
$=(x / 3-y+5 z)\left(x^{2} / 9+y^{2}+25 z^{2}+x y / 3+5 y z-5 z x / 3\right)$
$\therefore \frac{1}{27} \mathrm{x}^{3}-\mathrm{y}^{3}+125 \mathrm{z}^{3}+5 \mathrm{xyz}$
$=(x / 3-y+5 z)\left(x^{2} / 9+y^{2}+25 z^{2}+x y / 3+5 y z-5 z x / 3\right)$
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All Study Material
- 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
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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