Algebra 1

Algebra 1 Algebra 1 Till now we have learned about literals ( numbers) and different mathematical operations were performed on those literals like addition, subtraction, multiplication and division. Now we are going to learn about the Algebra. What is algebra? It is basically expressing the statements including different objects in different quantities in form of mathematics.

Before we study Algebra 1, we must know what all are constants and the variables. Any quantity whose value is fixed and does not change are called constants and the quantities expressed with some or the alphabets and can hold different values at different times are called variables.When we combine together the constants and the variables with some or the other mathematical operators i.e. +, - , * or / are called algebraic expressions. Some of the examples of algebraic expressions are x + y , 3x + z , 2x + 4y etc.

Some times the combination of variables with the same variable or the combination of variables with some other variable are also made in order to form the expressions. Eg: xy + x2 , a3- b3 and many such expressions are also formed.

Factors of a term: Let us write a term say 3xy. This term is the product of 3 , x and y. So x, y and 3 are the factors of 3xy. This means that the 3xy is divisible by all these 3 factors.

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Co-efficient of any term is the numerical factor or simply it is called the co-efficient of the term.

Let us consider an expression say 4x3y, then we say that the numerical co –efficient of 4x3y is 4. If we have an expression say x, then its numerical co- efficient of x is 1. We say x and x3y as the literal factors. Any constant value has no literal factor. An expression with one term is called monomial eg: 3x, 4xy, 5a are all monomials, whereas the expression with two terms is called binomial eg: 4a + 5b, 2x + 5y are the binomials.

Similarly expressions with three terms are trinomials and the expressions with one or more than one terms are called polynomials. It clearly says that monomial, binomial, trinomial all are polynomials. If we write 3x + 4x, then it will not be considered as a binomial as it will result in 7x which means the expression is a monomial.

Now we will learn about like terms and unlike terms : The terms which have the same literal factor are all called like terms else they are called unlike terms. When the two terms are like then it is not necessary that its numerical co-efficient are equal. The numerical constants may be same or not. As if we write 3xy and 5xy, here the numerical co-efficient different ie. 3 and 5, but the literal factor of both the terms is xy, so they are like terms.

Here is the working rule to check if the terms are like or unlike : a)

First we check the algebraic part of the terms

b)

All the variables of the algebraic part of the terms are same.

c)

All the powers of the algebraic variables are also same.

d)

The order in which the variables are written are not considered.

e)

The numeric part is same or not does not effect if the term is like or unlike.

Till now we have learned about literals (numbers) and different mathematical operations were performed on those literals like addition, subtraction, multiplication and division. Now we are going to learn about the Algebra.

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What is algebra? It is basically expressing the statements including different objects in different quantities in form of mathematics.Before we study Algebra 1, we must know what all are constants and the variables. Any quantity whose value is fixed and does not change are called constants and the quantities expressed with some or the alphabets and can hold different values at different times are called variables.

When we combine the constants and the variables with some mathematical operators, i.e. +, - , * or / , these are called algebraic expressions. Some of the examples of algebraic expressions are x + y , 3x + z , 2x + 4y etc. Some times the combination of variables with the same variable or the combination of variables with some other variable are also made in order to form the expressions.

E.g.: xy + x2 , a3- b3 and many such expressions are also formed.Factors of a term: Let us write a term say 3xy. This term is the product of 3 , x and y. So x, y and 3 are the factors of 3xy. This means that the 3xy is divisible by all these 3 factors.

Co-efficient of any term is the numerical factor or simply it is called the co-efficient of the term.

Let us consider an expression say 4x3y, then we say that the numerical co –efficient of 4x3y is 4. If we have an expression say x, then its numerical co- efficient of x is 1. We say x and x3y as the literal factors.

Any constant value has no literal factor. An expression with one term is called monomial eg: 3x, 4xy, 5a are all monomials, whereas the expression with two terms is called binomial eg: 4a + 5b, 2x + 5y are the binomials. Similarly expressions with three terms are trinomials and the expressions with one or more than one terms are called polynomials. It clearly says that monomial, binomial, trinomial all are polynomials. If we write 3x + 4x, then it will not be considered as a binomial as it will result in 7x which means the expression is a monomial.

Now we will learn about like terms and unlike terms : The terms which have the same literal factor are all called like terms else they are called unlike terms. When the two terms are like then it is not necessary that its numerical co-efficient are equal. The numerical constants may be same or not. As if we write 3xy and 5xy, here the numerical co-efficient different i.e. 3 and 5, but the literal factor of both the terms is xy, so they are like terms.

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