Page 121 - Maths Skills - 7

Algebraic Expressions 119

INTRODUCTION
A combination of constants and variables connected by any of the four fundamental operators (+, –, × or ÷)
is called an algebraic expression. For example, 2x + 3, 4x – 5x + 7, etc. are all algebraic expressions.
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TERMS OF AN EXPRESSION
A constant, a variable or a combination of a constant and variable connected with the operations of multiplication
or division is called a term of the algebraic expression.
For example, 4x is one term as it can be written as 4 × x × x. Similarly 2xy – 7ab has two terms:
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2 × x × y and –7 × a × b. Thus, different terms are added to form an algebraic expression.

FACTORS OF A TERM
In an algebraic expression, each term is a combination of variables and constants. A constant factor is called a
numerical factor while a variable factor is known as a literal factor.
1 1
For example, in an algebraic expression 2x y – a b c two terms are 2x y and – a b c.
2 2
2 2
2
2
4 4
1
Factors are 2 × x × x × y and – × a × a × b × b × c
4
−1
where 2 and are numerical factors and x, y, a, b and c are all literal factors.
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Coefficients
In a term of an algebraic expression any of the factors with the sign of the term is called the coefficient of the
product of the other factors in that term.
For example, In 7xy, the coefficient of x is 7y and the coefficient of y is 7x and 7 is called the numerical coefficient
or the constant term.
Like and Unlike Terms

When the terms have the same algebraic factors, they are called like terms. When the terms have different algebraic
factors, they are called unlike terms.
For example, in the algebraic expression 3ab – 2p + 7ab + 7p, 3ab and +7ab are like terms and –2p and 7p are
like terms. 3ab and –2p are unlike terms.

DEGREE OF AN EXPRESSION
Polynomials or algebraic expressions like 4x + 2y + z and 6a – 4b – 3c are trinomials with three variables.
Similarly, 2x – 3y and 5b – 2c are binomials with two variables. If you notice, all these expressions have index or
power of one.
3a + 5a – 7 is also a trinomial with one variable (a) but the power of one term, i.e., 3a is 2 and other term 5a is
2
2
1. This is a polynomial of degree 2.
Similarly, –3a + 5a + 2a – 1 is a quadrinomial with one variable (a) of degree 3.
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“The Term with the Highest Power in an Expression Decides the Degree of the Polynomial”
If an expression has two variables such as 2x y – 3xy + 5 then the degree of this expression will be 3 as x y is x y ,
2 1
2
2
i.e., highest power is 2 + 1 = 3. It means that if there is more than one variable in the same term, then the powers
are added to decide the degree of the term.
For example; ab has a degree 2. x y has a degree 5.
2 3
mn has a degree 4. a b has a degree 7.
3 4
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