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**.

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

● 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?

● 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?

● You have two exercise books. Your father gave you some more exercise books? How many exercise books are there with you now?

● Roby had 7 color pencils. He has lost some of them. How many color pencils he has now?

● Shelly’s age is 13 years.

(i) What was her age x years before?

(ii) What will be her age y years hence?

● Two less than one third of x

● One third of a

● Mike is 3 years older than his brother Rex. If Rex’s age is p years, what will be Mike’s age?

● The price of a dozen of banana is $ x. What will be the price of 4 dozen of bananas?

● The difference of two numbers is y, the greater number is 18. Find the smaller number.

● The product of two numbers is 64. One of them is d. Find the other.

● Your age is 12 years now. What was your age p year ago? What will be your age after p 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****From Algebraic Expression to HOME PAGE**