#### Solved Examples and Worksheet for Number of Terms in an Algebraic Expression

Q1Choose the value of the constant term in the expression, - 12x2 + 5x +4.
A. 4
B. - 12
C. 0
D. 5

Step: 1
- 12x2 + 5x + 4
[Original expression.]
Step: 2
A constant term is said to be the one which has no variables in it.
Step: 3
Therefore, 4 is the constant term in the expression - 12x2 + 5x + 4.
Q2Find the coefficient of x2 in the expression, 1 - x + 5 x2.
A. 5
B. 2
C. - 1
D. 1

Step: 1
In a term that is the product of a number and a variable, the number is called the coefficient of the variable.
Step: 2
The coefficient of x2 in the expression is 5.
Q3Find the number of terms in the algebraic expression - 5x + 6y - 3.
A. 2
B. 3
C. 8
D. 14

Step: 1
- 5x + 6y - 3 has the terms 5x, 6y and 3.
Step: 2
So, the number of terms in the expression - 5x + 6y - 3 is 3.
Q4Determine the number of terms in the algebraic expression 16 - m2 - n2 - 8mn + 4n.
A. 4
B. 2
C. 5
D. 8

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 5 terms in the algebraic expression 16 - m2 - n2 - 8mn + 4n.
Q5Determine the number of terms in the algebraic expression pqr - pq + qr - 9p2 - 2pr.

A. 8
B. 5
C. 12
D. 10

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 5 terms in the algebraic expression pqr - pq + qr - 9p2 - 2pr.
Q6Determine the number of terms in the algebraic expression x + 8 + xy - 6y.

A. 4
B. 5
C. 3
D. 0

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 4 terms in the algebraic expression x + 8 + xy - 6y.
Q7Determine the number of terms in the algebraic expression 7l - 12lm - 85 n .

A. 2
B. 3
C. 5
D. 4

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 3 terms in the algebraic expression 7l - 12lm - 85 n .
Q8Determine the number of terms in the algebraic expression 47a - 5ab + 115b + 3.

A. 4
B. 8
C. 2
D. 6

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 4 terms in the algebraic expression 47a - 5ab + 115b + 3..
Q9Determine the number of terms in the algebraic expression. 8q - 6pq + 11qr + 4pr - 13

A. 4
B. 8
C. 5
D. 2

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 5 terms in the algebraic expression 8q - 6pq + 11qr + 4pr - 13.
Q10Identify the number of terms in the expression, x2 - 10x + 6.
A. 5
B. 4
C. 8
D. 3

Step: 1
A term is either a single number or a variable or numbers and variables multiplied together.
Step: 2
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 3
So, there are 3 terms in the algebraic expression x2 - 10x + 6.
Q11Identify whether 'p2 + 5p - 12' is an equation or an expression or an inequality.
A. equation
B. inequality
C. expression
D. equation and expression

Step: 1
An expression is a mathematical phrase that combines numbers and/or variables using mathematical operations.
Step: 2
An equation is a mathematical sentence that uses the equal sign (=) to show that two expressions are equal.
Step: 3
An inequality is a mathematical sentence that uses symbols such as < , ≤, > , ≥ to compare two quantities.
Step: 4
Therefore, 'p2 + 5p - 12' is an expression.
[By the definition of Expression.]
Q12Which of the following is the variable of the expression? 6z3

A. z3
B. 6z3
C. z
D. 6z

Step: 1
Variables are letters or other symbols that represent unknown numbers or values.
Step: 2
So, 'Z' is the variable of the expression 6z3.
Q13Which of the following are the variables of the expression? 8xy

A. y, 8
B. 8, xy
C. x, y
D. x, 8

Step: 1
Variables are letters or other symbols that represent unknown numbers or values.
Step: 2
So, x, y are the variables of the expression 8xy.
Correct Answer is :   x, y
Q14Find the number of terms in the algebraic expression 3g2 - 8g3 + 6gh - 9g2h + 15.

A. 2
B. 5
C. 9
D. 7

Step: 1
Each term in an algebraic expression is separated by plus (+) or minus (-) symbol.
Step: 2
So, there are 5 terms in the algebraic expression 3g2 - 8g3 + 6gh - 9g2h + 15.
Q15Determine the number of terms in the algebraic expression 18 + x3 - 2xy + 5x2 -7 + 3y3
A. 5
B. 6
C. 8
D. 2

Step: 1
Each term in an algebraic expression is separated by plus (+) or minus (-) symbol.
Step: 2
18 + x3 - 2xy + 5x2 - 7 + 3y3
[Given expression.]
Step: 3
= x3 + 3y3 + 5x2 - 2xy + 11
[Simplify.]
Step: 4
So, the terms in the above expression are x3, 3y3, 5x2, 2xy, 11.
Step: 5
Therefore, the number of terms in the given algebraic expression is 5.