Algebraic Expressions and Identities
Expressions are formed from variables and constants.
Terms are added to form expressions. Terms themselves are formed as product of factors.
Whenever we add a positive number, we move to the right on a number line.
Whenever we add a negative number, we move to the left on a number line.
The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
In column method for addition, like terms are arranged in a column and addition is then done column-wise.
In horizontal method for addition, we collect all the like terms and then add them.
The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
In column method for subtraction of algebraic expressions, first write the expressions one below the other with the like terms appearing in the same column. Then change the sign of terms placed in second row.
In horizontal method for subtraction of algebraic expressions, first change the signs of the terms to be subtracted and then collect all the like terms and then add them.
If an equality is true for every value of the variable(s) present in the equality, it is called an identity.
A monomial multiplied by a monomial always gives a monomial.
When a polynomial is multiplied by a monomial we multiply every term in the polynomial by the monomial.
To multiply a polynomial by a binomial or trinomial each term of the polynomial is multiplied by every term in the binomial or trinomial.
To divide a monomial by a monomial, first express the numerator and the denominator in their irreducible form, and then cancel the common factors.
To divide a polynomial by a monomial either divides each term of the numerator by the denominator or factorizes the numerator and then, cancels the common factors.
To divide a polynomial by a polynomial either factorize the numerator and the denominator by using the appropriate method and then, cancel the common factors or follow long division method.