An algebraic expression is made up of the signs and symbols of algebra.
These symbols include the numerals, literal numbers, and the signs of operations (+, -, ×, ÷)
Definition of Algebraic Expression:
The combination of constants and variables, connected by signs of fundamental operations (+, -, ×, ÷) is called an algebraic expression.
For example:
x + y is an algebraic expression.
2x + 3y is an algebraic expression.
5a + 6c - b is an algebraic expression.
2x – 3y + 9z is an algebraic expression.
In the algebraic expression 3x² + 7y³ - 4xy.
3x², 7y³, -4xy are called terms of the expression.
An algebraic expression consists of two parts:
(i) Numerical Factor
(ii) Literal Factor
For example:
In the algebraic expression 7pqr, 7 is called numerical factor and p, q, r are called literal factors.
Monomial: An algebraic expression containing only one term is called a monomial.
For example; 3x, -7, ⁵/₉ a²bc are all monomials.
Binomial: An algebraic expression containing two terms is called a binomial.
For example; x – 7, 5x + 9y, ab + care all binomials.
Trinomial: An algebraic expression containing three terms is called a trinomial.
For example; x – y + 7, 3x + 4y – 5z, a³ + b² + c⁴ are all trinomials.
Multinomial: An algebraic expression containing two term is called a multinomial.
For example; x³ y² + 2x²y – 3xy + 7, a² + b² - 4c² - d², l + m + n – p are all multinomials.
Polynomial: In an algebraic expression, if the power of variables is a non-negative integer; then that expression is called a polynomial.
For example; 3x² + 4x + 7 is a polynomial.
x² + \(\frac{3}{x}\) is not a polynomial.
[The power of x in \(\frac{3}{x}\) is negative. Therefore, \(\frac{3}{x}\) = 3x\(^{-1}\)]
5√x + 2x² - 5 is not a polynomial.
[The power of x in 5√x is in fraction. Therefore, 5√x = 5x\(^{\frac{1}{2}}\)]
Note:
1. ab is a monomial, but a + b is a binomial.
2. 2ab is a monomial, but 2 + a + b is a trinomial.
3. 6abc is a monomial, but 6 + a + b + c is a quadrinomial or a polynomial of four terms.
● The sum of x and y.
x + y
● The subtraction of n from m.
m – n
● The product of a and b.
ab
● x divided by 4.
x/4
● 4 divided by m.
4/m
● The sum of 5 and p.
5 + p
● The product of z and 15.
15 × z
● 5 less than 3 times x.
3x + 5
● Half of the product of 4 and x.
4x/2
● One-tenth of y.
y/10
● 6 less than the sum of x and y.
(x + y) – 6
● The values of a and b is equal.
a = b
● The values of p is greater than of q.
P > q
● 8 is less than y.
8 < y
● p + q
The sum of p and q
● 5a
5 times of a
● x/6
1/6 the part of x.
● x + y + 1
The sum of x, y and 1
● 2p + r
The sum of r and two times of p
● m + 3x
The sum of m and three times of x
● a – 3b
Deduction of 3 times of b from a
● 3x – y
Deduction of y from 3 times of x
● (a + 2b)/3
1/3 of sum of a and two times b
● p/3 + 5
Sum of 1/3 rd portion of p and 5
● 9 > 2m
9 is greater than two times of m
● x + y < 10
Sum of x + y is less than 10
● Ben has $12, Kyle has $ x more. How many dollars does Kyle possess?
12 + x
● You worked out x sums yesterday. Today you have worked out 10 sums less. How many sum have you worked out today?
x – 10
● A taxi driver had earned a dollar on a day and $6 less on the next day. How much money has he earned on the next day?
a – 6
● Tom has 5 exercise books. His father bought x more exercise books for her. How many exercise books now Tom have?
5 + x
● Ron had 15 marbles, he lost y marbles. How many marbles are now remaining with him?
15 – y
● Kelly is x years older than John. The present age of John is y years. How old is Kelly now? What will be their ages after 5 years?
Kelly = y + x,
John = y + 5,
Kelly = y + x + 5
● A labourer earns $x daily. How much will he earn in 7 days?
7x
● There are x rows of trees in Harry’s garden. In each row there are 10 trees. How many trees are there in the garden?
10x
● You have two exercise books. Your father gave you some more exercise books? How many exercise books are there with you now?
2 + x
● Roby had 7 color pencils. He has lost some of them. How many color pencils he has now?
7 – x
● Shelly’s age is 13 years.
(i) What was her age x years before?
(ii) What will be her age y years hence?
(i) (13 – x) years
(ii) (13 + x) years
● Two less than one third of x
x/3 – 2
● One third of a
a/3
● Mike is 3 years older than his brother Rex. If Rex’s age is p years, what will be Mike’s age?
(p + 3) years
● The price of a dozen of banana is $ x. What will be the price of 4 dozen of bananas?
4x
● The difference of two numbers is y, the greater number is 18. Find the smaller number.
Smaller number = 18 – y
● The product of two numbers is 64. One of them is d. Find the other.
Other number = 64/d
● Your age is 12 years now. What was your age p year ago? What will be your age after p years?
Age before p years = (12 – y) years
Age after p years = (12 + y) years
1. Which of the following is not a monomial?
(i) p
(ii) 4
(iii) 5 xyz
(iv) 3pq + 3
Solution:
As a monomial contains one term, the options (i), (ii) and (iii) are monomials. But, the option (iv) is not a monomial.
● Algebraic Expression
Addition of Algebraic Expressions
Subtraction of Algebraic Expressions
Multiplication of Algebraic Expression
Division of Algebraic Expressions
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