Informative line

# 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: $$- 1$$

#### 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 $$y$$.

#### 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 $$2$$.

#### 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.

#### 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.

#### 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 $$x+ 3$$.

#### 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.

#### 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