Forming Expressions using Terms in Algebra

Forming Expression Using Factors & Terms

        An algebraic expression can have one term, two terms or more than two terms. An expression with one term is called a monomial, two terms is called a binomial and three terms is called a trinomial.  An expression with one or more terms is called a polynomial. 

        For example, the expression 2x is a monomial, 2x + 3y is a binomial,  and 2x + 3y + 4z is a  trinomial. All the expressions given above are polynomials.

A term may be any one of the following: 

        i)      a constant such as 8, −11, 7, −1,… 

        ii)     a variable such as x,a,p,y,… 

        iii)    a product of two or more variables such as xy, pq, abc, ... 

        iv)    a product of constant and a variable/variables such as 5x, −7pq, 3abc,…

Questions for Practice

1.  Identify the variables, terms and number of terms in each of the following expressions: 

            (i) 12−x   (ii) 7 + 2y   (iii) 29+3x+5y    (iv) 3x–5+7z 

2.  Find the numerical co-efficient of the following terms.  Also, find the co efficient of x and y in each of the term: 

            3x,  - 5xy,  - yz, 7xyz, y, 16yx. 

3.  If x  = 3, y = 2 find the value of  (i) 4x + 7y  (ii)  3x + 2y − 5  (iii)  x − y

4.  Find the value of  

        (i) 3m + 2n          (ii) 2m − n          (iii) mn − 1,     given that m = 2, n =  − 1. 

5.  Fill in the blanks: 

        (i) The variable in the expression 16x − 7 is ________. 

        (ii) The constant term of the expression 2y − 6 is _________. 

        (iii) In the expression 25m + 14n, the type of the terms are ________ terms. 

        (iv) The number of terms in the expression 3ab + 4c –9 is ________. 

        (v) The numerical co-efficient of the term  −xy is ________.

6.  Say True or False. 

        (i) x + ( −x) = 0 

        (ii) The co-efficient of ab in the term 15abc is 15. 

        (iii) 2pq and  − 7qp are like terms 

        (iv) When y = −1, the value of the expression 2y − 1 is 3 

7.  Find the numerical coefficient of each of the following terms: 

            −3yx, 12k, y, 121bc, − x, 9pq, 2ab 

8.  Write the variables, constants and terms of the following expressions. 

        (i)18 + x − y          (ii) 7p − 4q + 5           (iii) 29x + 13y         (iv) b + 2 5. 

9.  Identify the like terms among the following : 

            7x, 5y, −8x, 12y, 6z, z, −12x, −9y, 11z. 

10.  An algebraic statement which is equivalent to the verbal statement “Three times the sum of x and y” is 

        (i) 3(x + y)         (ii)  3 + x + y         (iii)  3x + y         (iv) 3 + xy