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Common Algebra Formulae

Following are the most commonly and widely used algebra equations.

1) (a+b)2=a2+b2+2ab
2) (a-b)2=a2+b2-2ab
3) (a+b+c)2=a2+b2+c2+2ab+2bc+2ca
4) (a+b)(a-b)= a2-b2
5) (a+b)3= a3+b3+3ab(a+b)
6) (a-b)3= a3-b3-3ab(a-b)
7) (a+b)2-(a-b)2=4ab
8 ) (a+b)2+(a-b)2=2(a2+b2)

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What is the dimensional formula for Area of Square?

Area of Square (A)

Area of Square refers to the number of square units required to fill the square is called the area of square. Area is a derived physical quantity. A square metre is the area of a square whose each sides are 1 metre.

Area of the square = side × side  
So,
Area of the square = L × L=L2

Hence, Dimensional formula for Area of Square  =M0L2T0

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Explain the Fundamental Physical Quantities and Units

The fundamentals of physics form the basis for the study and the development of engineering and technology. Measurement consists of the comparison of an unknown quantity with a known fixed quantity. The quantity used as the standard of measurement is called ‘unit’.

Fundamental physical quantities
Fundamental quantities are the quantities which cannot be expressed in terms of any other physical quantity.

Example– length, mass and time.

Derived quantities
A derived quantity is a quantity that is based on the result of a systematic equation that includes any of the seven basic quantities, which are the kilogram, meter, second, ampere, kelvin, mole and candela.

Examples–Area (Square meter; M2), speed (meters per second; m/s) and Density (kg/m3).

Unit –
Unit is the reference used as the standard measurement of a physical quantity. The unit in which the fundamental quantities are measured are called fundamental unit and the units used to measure derived quantities are called derived units.

System of unit –
Group of units of all physical quantities are system of unit.

  • G.S. system – It is the centimetre gram second system which are units of length, mass and time.
  • P.S. system – it is foot pound second system. Britishers used this system.
  • K.S. System – it is metre kilogram second system. European countries like France use this system.
  • S.I. System – It is the international system of unit. It is universally accepted and has seven fundamental units.

There are seven fundamental units (base units) and two supplementary units.

  1. SI system of units-
Quantity Definition Unit Symbol
Fundamental quantities
Length The longest extent of anything as measured from end to end. Metre M
Mass A fundamental measure of the amount of matter in the object Kilogram Kg
Time Time is the dimension on which the evolution of state of a system is allowed to occur. Seconds S
Electric current Electric current is defined as the rate at which charge flows through a surface. Ampere A
Temperature A measure of the warmth or coldness of an object or substance with reference to some standard value. Kelvin K
Luminous intensity Luminous intensity is an expression of the amount of light power emanating from a point source within a solid angle of one steradian. Candela Cd
Amount of substance Amount of substance, also called material quantity, is a dimensionless expression of the number of particles in a sample. Mole Mol
Supplementary quantities
Plane angle Plane angle is angle between two line meeting at the vertex. Radian rad
Solid angle Solid angle is the angle subtended by the object in three dimensional space from a point. Steradian sr
Wavelength Solid angle is the angle subtended by the object in three dimensional space from a point. Angstrom A0 = 10-8 cm

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