Algebraic Expressions:

Algebraic Expressions:

Introduction to algebraic expressions:

In mathematics,an expression is a finite combination of symbols that are well-formed,according to the rules applicable in the context at hand. Algebraic expressions are formed from variables and constants.We simply use the combination of operations of addition, subtraction, multiplication and division on the variables and constants to form expressions. We are faced with this question most of the time-What are Algebraic Expressions?? In general terms it is easy to explain algebraic Expressions,"An algebraic expression consists of the signs and symbols."Algebraic expressions does not contain equal sign.In algebra, an expression may be used to designate a value, which value might depend on values assigned to variables occurring in the expression; the determination of this value depends on the semantics attached to the symbols of the expression. These semantic rules may declare that certain expressions do not designate any value; such expressions are said to have an undefined वलुए.Another way of understanding the concept of Algebraic Expression is by looking at a few example problems of Algebraic Expression,similarly given below are few practice problems on algebraic expressions.

Some examples of algebraic expressions:

2x + 2y , 2xy , x2 - y2 , 3m + n - 5.
There are one or more terms in the algebraic expressions. For example, 3x2 + 4x + 2 is algebraic expression. It has three terms.

Let us discuss about some example problems on Algebraic expressions.

Example Problems - Algebraic Expressions
Problem 1:
Find the number of terms in the algebraic expression. 6x - 7
Solution:
The given expression 6x - 7 has two terms.
Problem 2:
Find the number of terms in the algebraic expression. a2 - 2ab + b2
Solution:
The given expression a2 - 2ab + b2 has three terms.
Problem 3:
What is the coefficient of x2 in the given algebraic expression? 5x2 + 2x + 6
Solution:
The coefficient of x2 is 5 in the expression.
Problem 4:
Add the two algebraic expressions: 3x + 21 and 4x + 7
Solution:
Sum of the two algebra expressions: 3x + 21 + 4x + 7
Rearrange the expression by grouping like terms.
3x + 4x + 21 + 7
Adding like terms in the expression.
7x + 28
Hence, 3x + 4x + 21 + 7 = 7x + २८
Problem 5:
Add the two algebraic expressions: 8x + 11 + 6z and 5x – 7
Solution:
Sum of the two expressions: 8x + 11 + 6z + 5x – 7
Rearrange the expression by grouping like terms.
8x + 5x + 6z + 11 – 7
Adding like terms in the expression.
13x + 6z + 4
Hence, 8x + 11 + 6z + 5x - 7 = 13x + 6z + 4
Problem 6:
Simplify the algebraic expression: (3a2 + 5a – 9) – (8a – a2 – 7)
Solution:
The given expression: (3a2 + 5a – 9) – (8a – a2 – 7)
Expand the expression.
3a2 + 5a – 9 – 8a + a2 + 7
Rearrange the expression by grouping like terms.
3a2 + a2 + 5a – 8a – 9 + 7
Adding like terms in the expression.
4a2 – 3a - 2
Hence, (3a2 + 5a – 9) – (8a – a2 – 7) = 4a2 – 3a - 2.
Problem 7:
Evaluate the algebraic expression b3 + 6b2 + 6b – 4 when b = -3
Solution:
We get a value for the algebraic expression when we substitute b is – 3.
b3 + 6b2 + 6b – 4
=(-3)3 + 6(-3)2 + 6(-3) – 4
= + 6 – 18 - 4
= -27 + 6(9) – 18 – 4
= -27 + 54 – 18 – 4
= - (27 + 18 + 4) + 54
= - 49 + 54
= 5.

Practice Problems - Algebraic Expressions:

Problem 1:
Find the number of terms in the expression. 64mn - 8
Answer:
Two terms.
Problem 2:
Find the number of terms in the expression. 6x2 - 3xy + 8y2 + 6
Answer:
Four terms.
Problem 3:
What is the coefficient of x in the given algebraic expression? 10x2 + 20x + 8
Answer:
20 .
Problem 4:
Add the two expressions: 6ab + 5a + 2ab and 7a - 5
Answer:
8ab + 12a - 5
Problem 5:
Simplify the algebraic expression: a2 + 2ab + b2 + 5ab + 2b2
Answer:
a2 + 7ab + 3b2
Problem 6:
Evaluate the algebraic expression: 10x2 + 20x when x = 2.
Answer:
80.

Hope you like the above example of Algebraic Expressions.Please leave your comments, if you have any doubts.