Algebraic Expressions
A
mathematical statement which is obtained by using mathematical fundamental
operation between constants and variables with different powers is called an
algebraic expression.
For
example:
- The sum of 2 and x is 2 + x, where the constant
2 and variable x is connected by ‘+’ sign.
- So, 2 + x is an algebraic expression.
- Similarly, other algebraic expressions are
2xy, 3x + 4y, x – y^{2} + 4 , etc.
Algebraic Terms
The parts of an algebraic expression separated by ‘+’
or ‘–’ signs are called algebraic terms.
For
example:
- 3x + 2y is an algebraic expression, where
3x and 2y are two parts connected by ‘+’ sign. So, 3x and 2y are called the
terms of the expression 2x + 3y.
Types of algebraic expression
Algebraic expressions are of different types. They are:
Monomial, Binomial, Trinomial and multinomial expressions.
- Monomial
Expression: An
algebraic expression which contains only one term is called a monomial
expression. For example: 4x, 3x^{2}y, -7xyz^{2}, etc.
- Binomial
Expression: An algebraic
expression which contains two terms connected by ‘+’ or ‘–’ is called a
binomial expression. For example: a + b, 2a^{2} – 3abx^{2}, 3x
– 4ay^{2}, etc.
- Trinomial
Expression: An
algebraic expression which contains three terms connected by ‘+’ or ‘–’ is
called a trinomial expression. For example: x + 2y – z, a^{2} + 2ab + b^{2},
etc.
- Multinomial
Expression: An
algebraic expression which contains four or more than four terms connected by
‘+’ or ‘–’ is called a multinomial expression. For example: 2x – 2y + z, x^{3}
– a^{2} + 2ab – b^{2} + 7, etc.
Coefficient, base and power
- Coefficient: A numerical or
constant quantity placed before the variable and multiplying it is called the
coefficient. For example: In an expression 3x, 3 is called the coefficient of
x.
- Base: An alphabet letter
used in algebraic expression is called the base. For example: In an expressioin
3x^{2}, x is the base.
- Power: The repeatation of
the same variable for the required number of times in an algebraic expression
is called power. For example: In an expressioin 3x^{2}, 2 is the power
of x.
Like and Unlike Terms
- Like
Terms:
The terms are like if the terms have the same base with same power of the
variable. For example: 2a, -3a, 4a are like terms. x^{3}, 2x^{3},
-5x^{3}, -3x^{3} are like terms. similarly 7xy, -3xy, 2xy are
like terms.
- Unlike
Terms:
The terms are unlike if the terms have the different variables or different
powers of the base. For example: x, 2x^{2}, 3x^{2}y, -y are
unlike terms. x^{3}, x^{4}, x^{-3}, -x are unlike
terms. Similarly xy, 2xz, 3x^{2}y are unlike terms.
Values of Algebraic Expressions
When we substitute the value of a variable in an
algebraic expression with a number, the value of the expression is obtained
after use of mathematical fundamental operations, it is called the value of the
expression.
For
example: if
x = 2 and y = 3, find the value of 2x – 3x^{2}y.
Here, the given expression = 2x – 3x^{2}y
= 2 × 2 – 3 × 2^{2} × 3
= 4 – 3 × 4 × 3
= 4 – 36
Workout Examples
Example 1: Write the type of each
expression.
a.
4x
b.
2a
+ 3b
c.
3x^{2}
– 4xy + 2y^{2}
d.
9x^{3}
– 10x^{2} + 4x – 21
e.
3x^{3}
– 2x^{2} + 5x + 7xy - 8
Solution: Here,
a. 4x -------> Monomial
b. 2a + 3b ---------> Binomial
c.
3x^{2}
– 4xy + 2y^{2} ---------> Trinomial
d.
9x^{3}
– 10x^{2} + 4x – 21 ----------> Multinomial
e.
3x^{3}
– 2x^{2} + 5x + 7xy – 8 ----------> Multinomial
Example 2: Rewrite the following
statements in algebraic expressions.
a.
The
sum of twice x and 5.
b.
Three
times the difference of x and y is less than 3a.
c.
5x
is added to the product of b and 7.
d.
One
fourth of x is added to 25
e.
7x
is divided by 14 and added to product of c and 4.
Solution: Here,
a. 2x + 5
b. 3(x – y) < 3a
c.
5x + 7b
d.
x/4 +25
e.
7x/14 +4c
Example 3: Write the terms having:
a.
Base
= x, power = 2 and coefficient = 1
b.
Base
= x, power = 3 and coefficient = -3
c.
Base
= y, power = 5 and coefficient = 4b
d.
Base
= z, power = 2 and coefficient = -a
Solution: Here,
a. x^{2}
b. -3x^{3}
c.
4by^{5}
d.
–az^{2}
Example 4: Identify the like and unlike
terms of the following expressions:
a.
3x,
-2x, 7x
b.
3a^{2},
3a^{3}, 4a
c.
2(x+y),
3(x+y)^{3}, 9(x+y)^{2}
Solution: Here,
a. Like terms
b. Unlike terms
c.
Unlike
terms
Example 5: If x = 4 and y = 3, find the
value of 2xy + 3y^{2}
Solution: Here,
x = 4
y = 3
∴ 2xy + 3y^{2} = 2 × 4 ×3 + 3 × 3^{2}
= 24 + 3 × 9
= 24 + 27
= 51You can comment your questions or problems regarding the algebraic expressions here.
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