Algebraic Expression

What is an Algebraic Expression?

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.

Classification of Algebraic Expressions:

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.

A. Express the following algebraic expressions with the help of signs and symbols:

● 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

B. Express the following algebraic expressions in words:

● 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

C. Express the following algebraic expressions using symbol if it is necessary.

● 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

Solved Examples on Algebraic Expression:

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

Algebraic Expression

Addition of Algebraic Expressions

Subtraction of Algebraic Expressions

Multiplication of Algebraic Expression

Division of Algebraic Expressions

8th Grade Math Practice

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