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1.Algebra Tutor
2.The Fun Way to Learn Algebra

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1. Introduction to various concepts of algebra

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1. Introduction to various concepts of algebra

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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:

B. Express the following algebraic expressions in words:

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?

● 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

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Addition of Algebraic Expressions Subtraction of Algebraic Expressions Multiplication of Algebraic Expression Division of Algebraic Expressions

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Algebraic Expression | Algebraic Expressions in Words | Classification

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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.

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The Degree (for a polynomial with one variable, like x) is:

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Online quiz

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