Question:
Find the value
$8 x^{3}+27 y^{3}-216 z^{3}+108 x y z$
Solution:
$=(2 x)^{3}+(3 y)^{3}+(-6 y)^{3}-3(2 x)(3 y)(-6 z)$
$=(2 x+3 y+(-6 z))\left((2 x)^{2}+(3 y)^{2}+(-6 z)^{2}-2 x+3 y-3 y(-6 z)-(-6 z) 2 x\right)$
$=(2 x+3 y+(-6 z))\left(4 x^{2}+9 y^{2}+36 z^{2}-6 x y+18 y z+12 z x\right)$
$? 8 x^{3}+27 y^{3}-216 z^{3}+108 x y z$
$=(2 x+3 y+(-6 z))\left(4 x^{2}+9 y^{2}+36 z^{2}-6 x y+18 y z+12 z x\right)$
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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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