Algebra is one of the oldest branches of mathematics, dealing with number theory, geometry, and analysis. It is characterized by some as the analysis of mathematical symbols and rules, as well as the manipulation of these mathematical symbols.
Algebra also covers a wide range of subjects, from fundamental problem solving to abstraction studies. Basically concentrated on variables with unknown values. The branch of mathematics is concerned with variables and arithmetic operations performed over these symbols. These variables have no set values. In our daily lives, we encounter problems. Certain values are always changing.
Expression is a combination of terms that are combined together using mathematical operations such as subtraction, addition, multiplication, and division.
- A constant is a number or numerical figure that has a fixed value.
- A variable is a symbol with an unfixed value.
- A term is defined as a constant, a single variable, or a combination of a variable and a constant combined with multiplied or division.
Examples of Expression in Algebra: 2x+5, 6x + 12, and so on …
Variables: A variable is an alphanumeric character that represents a numerical value or a number. A variable in algebra is used to represent an unknown amount of unknown values.
Most often, the alphabets ‘a’,’b’,’c’,’x’,’y’, and ‘z’ are used as variables in equations. The term variable refers to the value of another variable or equation.
For Example,
in equation,
3y + 11 = 20
y → Variable
3 → coefficient of y
11 and 20→ constants
‘+’ → operator
Question: What is the value of the expression 9+4n – 1 when n equals 3?
Answer:
Here Given Expression : 9+4n – 1
and n = 3
therefore , we will put the value of n = 3 in above given expression:
= 9 + 4n – 1
= 9 + 4(3) – 1
= 9 + 12 – 1
= 21 – 1
= 20
so the value of expression is 20 .
Sample Problems
Problem 1: What is the value of the expression n2 + 5n – 5 when n equals 2?
Solution:
Here Given Expression: n2 + 5n – 5
and n = 2
therefore , we will put the value of n = 2 in above given expression:
= n2 + 5n – 5
= 22 + 5(2) – 5
= 4 + 10 – 5
= 14 -5
= 9
so the value of expression is 9 .
Problem 2: What is the value of the expression 4x + 7 when x equals 3?
Solution:
Here Given Expression: 4x + 7
and x = 3
therefore , we will put the value of n = 2 in above given expression:
= 4x + 7
= 4(3) + 7
= 12 + 7
= 19
so the value of expression is 19 .
Problem 3: What is the value of the expression (n + 2)2 when n equals -2?
Solution:
Here Given Expression : (n + 2)2
and n = -2
therefore , we will put the value of n = – 2 in above given expression:
= (n + 2)2
By using algebraic expression , we will simplify (a + b)2 = a2 + 2ab + b2
= n2 + 2(n)(2) + 22
now put the value of n= -2 in above expression
= (-2)2 + 2(-2)(2) + 4
= 4 + (-8) + 4
= 4 – 8 +4
= 8 – 8
= 0
so the value of expression is 0 .
Problem 4: What is the value of the expression 20 – 4n when n equals 4?
Solution:
Here Given Expression : 20 – 4n
and n = 4
therefore , we will put the value of n = 4 in above given expression:
= 20 – 4n
= 20 – 4(4)
= 20 – 16
= 4
so the value of expression is 4 .
Problem 5: What is the value of the expression x2(5 – x) when x equals 3?
Solution:
Here Given Expression: x2(5 – x)
and x = 3
therefore , we will put the value of x = 3 in above given expression:
= x2(5 – x)
= 5x2 – x3
= 5(3)2 – 33
= 5(9) – 27
= 45 – 27
= 18
so the value of expression is 18 .
Problem 6: What is the value of the expression 3x + 4y + 20 when x = 3 , y = 2?
Solution:
Here Given Expression: 3x + 4y + 20
and x = 3 , y = 2
therefore , we will put the value of x = 3 , y = 2 in above given expression :
= 3x + 4y + 20
= 3(3) + 4(2) + 20
= 9 + 8 + 20
= 17 + 20
= 37
so the value of expression is 37 .