Question:
Find the value
$4(x-y)^{2}-12(x-y)(x+y)+9(x+y)^{2}$
Solution:
Let $(x-y)=x,(x+y)=y$
$=4 x^{2}-12 x y+9 y^{2}$
Splitting the middle term - 12 = – 6 - 6 also 4 × 9 = −6 × − 6
$=4 x^{2}-6 x y-6 x y+9 y^{2}$
$=2 x(2 x-3 y)-3 y(2 x-3 y)$
$=(2 x-3 y)(2 x-3 y)$
$=(2 x-3 y)^{2}$
Substituting x = x - y & y = x + y
$=[2(x-y)-3(x+y)]^{2}=[2 x-2 y-3 x-3 y]^{2}$
$=(2 x-3 x-2 y-3 y)^{2}$
$=[-x-5 y]^{2}$
$=[(-1)(x+5 y)]^{2}$
$=(x+5 y)^{2} \quad\left[?(-1)^{2}=1\right]$
$\therefore 4(x-y)^{2}-12(x-y)(x+y)+9(x+y)^{2}=(x+5 y)^{2}$
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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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