Informative line

Parts Of An Expression

Terms of an Expression

  • The terms of an expression are either a single number or a variable, or numbers and variables multiplied together.
  • These are separated using '+' and '–' signs.

For example: \(3x^2 + 4x - 1\)

There are \(3\) terms:

First term: \(3x^2\)

Second term: \(4x\)

Third term: \(- 1\)

 

Illustration Questions

How many terms are there in  \(4x^3 + 3x^2 - 2x+1\)?

A \(1\)

B \(2\)

C \(3\)

D \(4\)

×

Terms are separated by '+' and '–' signs.

There are \(4\) terms in  \(4x^3 + 3x^2-2x+1\)

First term: \(4x^3\)

Second term: \(3x^2\)

Third term: \(- 2x\)

Fourth term: \( 1\)

Hence, option (D) is correct.

How many terms are there in  \(4x^3 + 3x^2 - 2x+1\)?

A

\(1\)

.

B

\(2\)

C

\(3\)

D

\(4\)

Option D is Correct

Unlike Terms

  • The terms which do not have same literal factors are known as unlike terms.

For example: 

1) \(5xy^2\) and \(5x^2y\) are unlike terms as they do not have same literal factors because the power of \(x\) and \(y\) are not same in the terms.

2) \(5x\) and \(5y\) are unlike terms as they do not have same literal factors because in \(5x\), the literal factor is \(x\) whereas in \(5y\), it is \(y\).

Illustration Questions

Which one of the following is an unlike term of \(5yz\)?

A \(- 7yz\)

B \(6zy\)

C \(- 5 y^2z\)

D \(10yz\)

×

Unlike terms do not have same literal factors.

\(5yz\) and \(-5y^2z\) do not have same literal factors because the power of \( y\) is not same in the terms.

Thus, they are unlike terms. 

Hence, option (C) is correct. 

Which one of the following is an unlike term of \(5yz\)?

A

\(- 7yz\)

.

B

\(6zy\)

C

\(- 5 y^2z\)

D

\(10yz\)

Option C is Correct

Constant Term

  • A term of an expression having no literal factor is called constant term.

For example: \(x^2 + y^2+ 2\)

Here, \(2\) is the term which does not have a literal factor.

Thus, the constant term is \(2\).

Illustration Questions

Which is the constant term in \(x^3-x^2 + 3\)?

A \(x^3\)

B \(3\)

C \(x^2\) 

D \(Both\,x^3 and \,x^2\)

×

Given: \(x^3-x^2 + 3\)

 

A constant term does not have variables.

Here, \(3\) is the term which does not have a literal factor.

Thus, the constant term is  \(3\).

Hence, option (B) is correct.

Which is the constant term in \(x^3-x^2 + 3\)?

A

\(x^3\)

.

B

\(3\)

C

\(x^2\) 

D

\(Both\,x^3 and \,x^2\)

Option B is Correct

Numerical Factor

Factors

  • When two or more numbers and variables are multiplied, each one of them is called a factor of the product.

For example: \(5x\)

Here, \(5\) and \(x\) are factors of \(5x\).

Numerical factor

  • A constant factor is called numerical factor.

For example: \(5xy^2\)

Here, \(5\) is a numerical factor of \(5xy^2\).

Note: A numerical factor can be a whole number, an integer, a fraction or a decimal.

Illustration Questions

What is the numerical factor of \(- 7xy^2\)?

A \(x\)

B \(2\)

C \(y\)

D \(-7\)

×

Given: \(-7xy^2\)

 

A numerical factor is a number used in the expression.

Here, constant factor is \(-7\).

Thus, \(-7\) is the numerical factor of \(-7xy^2\).

Hence, option (D) is correct.

What is the numerical factor of \(- 7xy^2\)?

A

\(x\)

.

B

\(2\)

C

\(y\)

D

\(-7\)

Option D is Correct

Like Terms

  • The terms which have the same literal factors are called like terms.

For example: 

1) \(3xyz\) and \(-6xyz\)  are like terms as they have same literal factors \((xyz)\) having the same power.

2) \(6x^2y^3\) and \(-16 x^2 y^3\) are like terms as they have same literal factors \(x^2y^3\) having the same power.

 

Illustration Questions

Which is the like term of \(3x\)?

A \(-6x\)

B \(2y\)

C \(3\)

D \(2z\)

×

Like terms have same literal factors with same power.

\(3x\) and \(-6x\) have the same literal factors because the power of \(x\) is same in both the terms.

Thus, the like term of \(3x\) is \(-6x\).

Hence, option (A) is correct.

Which is the like term of \(3x\)?

A

\(-6x\)

.

B

\(2y\)

C

\(3\)

D

\(2z\)

Option A is Correct

Coefficients

  • In a product of numbers and variables, every factor is the coefficient of all other remaining factors.

For example: (i) \(3xyz\)

Here, \(3yz\) is the coefficient of \(x\).

\(3xy\) is the coefficient of \(z\).

\(3xz\) is the coefficient of \(y\).

(ii) \(5 (x+3)\)

Here, \(x+3\) is the coefficient of \(5\).

\(5\) is the coefficient of \(x+ 3\).

Illustration Questions

What is the coefficient of \(y^2\) in \(8 xy^2z\) ?

A \(8\)

B \(xz\)

C \(y^2\)

D \(8xz\)

×

In a product of numbers and variables, every factor is the coefficient of all other remaining factors.

The coefficient of \(y^2\) in \(8xy^2z\) is \(8xz\).

Hence, option (D) is correct.

What is the coefficient of \(y^2\) in \(8 xy^2z\) ?

A

\(8\)

.

B

\(xz\)

C

\(y^2\)

D

\(8xz\)

Option D is Correct

Literal Factor

  • In any given expression, the variable is known as literal factor.

For example: \(3xyz^2\)

Here, \(x\)\(y\) and \(z^2\) are literal factors of the given expression.

Illustration Questions

Which one of the following is NOT a literal factor of \(25 xyz\) ?

A \(x\)

B \(y\)

C \(25\)

D \(z\)

×

Given: \(25 xyz\)

 

A literal factor is a variable.

Here, \(25\) is a numerical factor and \(x, \; y\) and \(z\) are literal factors.

Thus, \(25\) is not a literal factor.

Hence, option (C) is correct.

Which one of the following is NOT a literal factor of \(25 xyz\) ?

A

\(x\)

.

B

\(y\)

C

\(25\)

D

\(z\)

Option C is Correct

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