Algebraic Expression

What is an algebraic expression?

The combination of constants and variables, connected by signs of fundamental operations (+, -, ×, ÷) is called 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.

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\(^{\frac{1}{2}}\)]

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

● 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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