Solved Examples based on Algebraic Expressions

Example 1: Determine the variable, coefficient, constant, and terms of the algebraic expression 31mn – 16m + 4n + 19.

Solution:

Given expression: 31mn – 16m + 4n + 19

= 31mn + (–16m) + 4n + 19

Variables: mn, m, and n.

Terms: 31mn, (–16m), 4n, and 19.

Constant: 19

Coefficients: 31 is the coefficient of mn, 

–16 is the coefficient of m, and 

4 is the coefficient of n.

Example 2: Identify the terms, like terms, coefficients, and constants in the expressions given below.

a) 8xy − 13x² + 14x + 5y − 21

b) x² + 5x + 7 − 15x 

Solution:

a) Given expression: 8xy − 13x² + 14x + 5y − 21

= 8xy + (−13x²) + 14x + 5y + (−21)

The terms of the given expression are 8xy, (−13x²), 14x, 5y, and (−21). 

We know that like terms are those that have the same variables.

The given expression doesn’t have any like terms.

Constant: (−21).

8 is the coefficient of xy, (−13) is the coefficient of x², 14 is the coefficient of x, and 5 is the coefficient of y.

Hence, the coefficients are 8, (−13), 14, and 5.

b) Given expression: x² + 5x + 7 − 15x 

= x² + 5x + 7 + (−15x)

The terms of the given expression are x2, 5x, 7, and (−15x).

We know that like terms are those that have the same variables.

Here the like terms are 5x and (−15x).

Constant: 7.

1 is the coefficient of x², 5 is the coefficient of x, and (−15) is the coefficient of x.

Hence, the coefficients are 1, 5, (−15).

Example 3: Determine the value of y in the equation 5y − 13 = 2y + 17.

Solution:

Given,

5y − 13 = 2y + 17

⇒5y − 2y = 17 + 13

⇒ 3y = 30

⇒ y = 30/3

⇒ y = 10.

Therefore the value of y in the equation 5y − 13 = 2y + 17 is 10.

Example 4: Identify the terms, like terms, coefficients, and constants of the algebraic expression 10x³ + 71x² + 91x − 20x² + 61.

Solution:

Given expression: 10x³ + 71x² + 91x − 20x² + 61

= 10x³ + 71x² + 91x + (−20x²) + 61.

Terms: 10x³, 71x², 91x , (−20x²), and 61.

Constant: 61

Coefficients: 10 is the coefficient of x³, 71 is the coefficient of x², 91 is the coefficient of x, and (−20) is the coefficient of x².

Like terms: 71x² and (−20x²).

Let us learn about what an algebraic expression is before learning about the terms of an algebraic expression. An algebraic expression is a concept of expressing numbers by using letters such as a, b, m, n, x, y, z, etc. without specifying their actual values.

An algebraic expression is a mathematical statement where variables have been combined using basic arithmetic operations such as addition, subtraction, multiplication, or division. The variables are the unknown values such as a, b, x, y, z, etc. A coefficient is a value that is placed before and multiplied by a variable, while a constant is the fixed numerical value.