6th Class Mathematics Algebra Identification of Terms of the Algebraic expression

    Identification of Terms of the Algebraic expression  

Literals or Variables

Alphabetical symbols are used in mathematics called variables or literals, \[a,\text{ }b,\text{ }c,~~~d,\text{ }m,\text{ }n,\text{ }x,\text{ }y,\text{ }z\text{ }..........,\]etc. are some common letters used for variables.        

Constant terms

The symbols which itself indicate a permanent value is called constant. All numbers are called constant. \[6,10,\frac{10}{11},15,-6,\sqrt{3}.......\]etc. are constant because, the value of the number does not change or remains unchanged. Therefore it is called constant.  

  Variable Terms  

A term which contains various numerical values is called variable term. Product of 4 and\[\text{ }\!\!~\!\!\text{ X=4 }\!\!\times\!\!\text{ X=4X}\] Product of \[\text{2,X,}{{\text{Y}}^{\text{2}}}\]and \[Z=2\times X\times {{Y}^{2}}\times Z=2X{{Y}^{2}}\] Product of  ?3, m and \[n=-3\times m\times n=-3mn\] Thus, \[4X,2X{{Y}^{2}}Z-3mn,\]are variable terms We also know that \[1\times X=X,1\times Y\times \text{ }z=YZ,-1\times {{a}^{2}}\times b\times c=-{{a}^{2}}\text{ }bc\]Thus\[\text{X,YZ,-}{{\text{a}}^{\text{2}}}\text{ bc}\]are variable terms  

Types of Terms  

There are two types of terms, like and unlike. Terms are classified by similarity of their variables.  

Like Term The terms having same variables are called like terms. \[\text{6X, X,-2X, }\frac{\text{4}}{\text{9}}\text{X,}\], are like terms, \[\text{ab,-ab,4ab,9ab,}\]\[\text{ab},-\text{ab,4ab,9ab,}\] are like terms. \[\text{2}{{\text{X}}^{\text{2}}}\text{,3}{{\text{X}}^{\text{2}}}\text{Y,}{{\text{X}}^{\text{2}}}\text{Y,}\frac{\text{10}}{\text{7}}{{\text{X}}^{\text{2}}}\text{Y}\]are like terms.  

Unlike Term   The terms having different variables are called unlike terms. \[\text{6X, 2}{{\text{Y}}^{\text{2}}}\text{,}-\text{9}{{\text{X}}^{\text{2}}}\text{YZ, 4XY,}\]are unlike terms. \[\text{9a,}-\text{b,3}{{\text{a}}^{\text{2}}}\text{,4ab,}\]are unlike terms. \[\text{6}{{\text{X}}^{\text{2}}}\text{,7ab,4}{{\text{a}}^{\text{2}}}\text{b,}\]are unlike terms.  

Coefficient                

The coefficient of every term is multiplied with the term. In term, \[-6{{m}^{2}}\text{ }np,\]coefficient of\[-6=m{{n}^{2}}\]p because \[m{{n}^{2}}\text{ }p\]is multiplied with ? 6 to form \[\text{-- 6m}{{\text{n}}^{\text{2}}}\text{p}\] similarly. Coefficient of \[{{m}^{2}}=-6np,\]coefficient of \[n=-6{{m}^{2}}p\] Coefficient of \[{{\text{m}}^{\text{2}}}\text{n}\,\,\text{p=}-6\]and Coefficient of \[-6\text{=}{{\text{m}}^{\text{2}}}\text{np}\text{.}\]  

Variable or Literal Coefficient

The variable part of the term is called its variable or literal coefficient. In term \[-\frac{\text{5}}{\text{4}}\text{abc,}\]variable coefficient is abc.  

Constant Coefficient

The constant part of the term is called constant coefficient. In term \[-\frac{\text{5}}{\text{4}}\text{ }\!\!~\!\!\text{ abc,}\] constant coefficient is \[-\frac{\text{5}}{\text{4}}\text{ }\!\!~\!\!\text{ }\text{.}\]  

Polynomials

An expression having two or more terms is known as polynomials. The expression \[3+5x\]is a polynomial and degree of the polynomial is the highest power of variable which presents in the term. In the expression, \[3+5x,x\]is the variable and its power is 1 therefore, the degree of the polynomial is 1.

\[5{{x}^{2}}+3{{y}^{3}}\](It is a polynomial in \[x\] and \[y\]and its degree is 3)

\[5{{x}^{2}}+3{{y}^{-3}}\] (It is not a polynomial as exponent if y is negative integer)  

Monomials

An expression which has one term is called monomials, ie. \[4y,3{{b}^{2}}\]

Binomials

An expression which has two terms is called binomials, ie. \[3{{b}^{2}}-4ac.\]

Trinomials

An expression which has three terms is called trinomials, ie. \[{{x}^{2}}-ac+3z\]

Quadrinomials

An expression which has four terms is called Quadrinomials. ie.\[~{{a}^{2}}-bc+x-5\]