Identification of Terms of the Algebraic expression

**Category : **6th Class

**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.\[~{{a}^{2}}-bc+x-5\]

*play_arrow*ALGEBRA*play_arrow*Introduction*play_arrow*Identification of Terms of the Algebraic expression*play_arrow*Operations on Algebraic Expressions*play_arrow*Algebra

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