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1. Identify the coefficient of each term of the given expression: 3x – 5xy + 7y – 6y + 9
2. Find out the like terms from the following:
3 2
2
2 2
2
3 2
3 3
3 2
a , a b , a b, 3a b , 7a b , 7ba, a b , 4b a .
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3. Simplify the given expression: 6a – 7ab + 4b – (b – 3ab + 2a )
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4. What is the value of 5x + 4x – 7 if x = –2?
5. If m = 10 and n = 18, find the number of saplings planted by Aman and Ria together in the
kitchen garden.
Algebraic Expression
A combination of constants and variables connected by the signs of mathematical operations +,
–, ×, ÷ is called an algebraic expression.
For example, x – 7; 5x + 1; 8xy + 3, etc. are all examples of algebraic expressions. Here the numbers
7, 5, 1, 8, 3 are constants and the letters x and y are variables.

Note: Letters like a, b, c, x, y, etc. are used as variables (literals), while numbers are the constants. The value
of a variable can vary, so the overall value of an expression changes depending on the variable’s value.

Terms, Factors, and Coefficients

The parts of an algebraic expression that are added together are called the terms of the expression.
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For example, in the algebraic expression 2x + 3y – 3y , there are three terms i.e., 2x, 3y, –3y added
together.
Each term of an algebraic expression can be formed as the product of factors. For example, in the
expression –17xyz, the numerical factor is –17, and the literal factors are x, y, and z.

A coefficient is a numerical factor that is written with the variable in a term. For example, in the
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term –5ab, the coefficient is –5, and the coefficient in the term 4x is 4.
Example 1: Identify the variable, constant, terms, factors, and coefficients of the variable terms
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in the given algebraic expression: 7x y + 3xy + 8. Expression 7x y + 3xy + 8
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Solution: The given expression is 7x y + 3xy + 8.
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Here, x and y are variables (so, 7x y and 3xy Terms 7x y 3xy 8
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are variable terms) and 8 is the constant term. [Variable term] [Variable term][Constant term]
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7x y is the product of factors 7, x, x, y; and 3xy

is the product of factors 3, x, y. Factors 7 x x y 3 x y
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The coefficients of terms 7x y and 3xy are 7 and [Coefficient [Coefficient
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3 respectively. of 7x y] of 3xy]
Like and Unlike Terms

In an algebraic expression, terms having the same variables and the same exponent are called
like terms. For example, 7xy, –5xy, 19xy, and xy are like terms.

In an algebraic expression, terms having different variables or the same variables with unequal
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exponents are called unlike terms. For example, 3xy, 5y, 4x , 5x, 2x y are unlike terms.
195 Algebraic Expressions