Table of contents  
How are Expressions Formed?  
Terms of an Expression  
Like and Unlike Terms  
Monomials, Binomials, Trinomials and Polynomials  
Finding the Value of an Expression 
Let's say you want to save money to buy a new bike that costs Rs 200. You decide to save a certain amount of money each week. For this, you can use an algebraic expression to figure out how many weeks it will take to save enough money.
If you save Rs10 every week, you can use the expression $10\mathit{x}=200$, where $\mathit{x}$ is the number of weeks.
By solving for $\mathit{x}$, you can determine that it will take 20 weeks to save Rs 200.
We use letters x, y, l, m, etc to denote variables. A variable can take various values. On the other hand constant has a fixed value. Examples of constants are 4, 100, etc
In math, an algebraic expression consists of numbers, variables, and basic operations like addition, subtraction, multiplication, division, and exponentiation with rational exponents.
Terms
Parts of an expression that are formed separately and then added (or subtracted) are called terms.Examples:
For the expression (4x + 5):
For the expression (4x^{2}  3xy):
Addition of Terms: Terms are added to form expressions. For example, in (4x^{2} 3xy), 4x^{2} + (3xy) = 4x^{2}  3xy.
The minus sign is included in the term to avoid confusion. In (4x^{2}  3xy), the term is (3xy), not (3xy).
In a term, the numerical factor is referred to as the numerical coefficient.
They indicate the scale or magnitude of the associated variables and help in simplifying expressions and solving equations efficiently.
Example: In the term 2x + 4y  9, the coefficient of x is 2, and the coefficient of y is 4.
(i) When the Coefficient of a term is 1:
(ii) When the Coefficient of a term is 1:
(iii) General Use of Coefficient:
(iv) Simplifying Expressions with Coefficients:
Like terms are combined by addition or subtraction
Example: Identify the terms and their factors in the following expressions:
Sol: (a) 5xy² + 7x²y
Terms are 5xy² and 7x²y
Factors are 5, x, y, y and 7, x, x, y.
(b) ab + 2b² – 3a²
Terms are ab, 2b², 3a²
Factors are 1, a, b, 2, b, b, 3, a, a.
(c) 1.2 ab – 2.4 b + 3.6 a
Terms are 1.2 ab, 2.4 b, 3.6 a
Factors are 1.2, a, b, 2.4, b, 3.6, a.
(d) 3/4 x + 1/4
Terms are 3/4 x and 1/4
Factors are 3/4, x and 1/4.
Example: Identify the numerical coefficients of terms (other than constants) in the following expressions:
Sol: (a) 1.2a + 0.8b
Coefficients are 1.2 for 1.2a, 0.8 for 0.8b.
(b) 3.14 r²
Coefficient of 3.14 r² is 3.14.
(c) 2 (l + b)
Coefficients are 2 for 2l and 2 for 2b.
Terms that have the same algebraic factors are called like terms. Terms that have different algebraic factors are called unlike terms.
Example: State whether a given pair of terms is of like or unlike terms.
Sol: (i) –7x, 5/2 x
Like terms (both have the variable x)
(ii) 4m²p, 4mp²
Unlike terms (different variable powers)
Algebraic expressions that contain only one term are called monomials. Algebraic expressions that contain only two unlike terms are called binomials. Algebraic expressions that contain only three unlike terms are called trinomials.
Algebraic expressions that have one or more terms are called polynomials. Therefore, binomials and trinomials are also polynomials.
Example: Classify into monomials, binomials, and trinomials.
Sol: (i) 1 + x + x²: Trinomial
Expression is Trinomial as it contains 3 terms: 1, x, and x²
(ii) a² + b²: Binomial
Expression is Binomial as it contains 2 terms: a² and b²
(iii) 7mn: Monomial
Expression is Monomial as it contains 1 term: 7mn
(iv) z² – 3z + 8: Trinomial
Expression is Trinomial as it contains 3 terms: z², 3z and 8
We can perform arithmetic operations on algebraic expressions. To add the like terms in an algebraic expression, multiply the sum of their coefficients with their common algebraic factors. To subtract the like terms in an algebraic expression, multiply the difference of their coefficients with their common algebraic factors. For example, let us subtract 9ab from 15ab
Thus, to add or subtract algebraic expressions, rearrange the terms in the sum of the given algebraic expressions, so that their like terms and constants are grouped. While rearranging the terms, move them with the correct '+' or ''sign before them.
Let us see this example.
Add 4x + 12 and 8x  9.
We know that the terms 4x and 8x are like terms and 12 and 9 are items.
Therefore,
= (4 + 8) x + 3
= 12x + 3
Unlike terms remain unchanged in the sum or difference of algebraic expressions.
Application of Algebraic Expressions
Algebraic expressions can be used to represent number patterns. In the following example, we can find the relation between several cones and the number of ice cream scoops.
Number of cones (n)  Number of ice  cream scoops (2n) 
1  2 
2  4 
3  6 
4  8 
15  2 x 15 
Thus, we can find the value of an algebraic expression if the values of all the variables in the expression are known.
Similarly, we can write formulas for the perimeter and area for different geometrical figures using simple, easytoremember algebraic expressions.
Area and perimeter of different shapes
• If s represents the side of a square, then :
=>The perimeter is 4s
=>The area is s^{2}
• If l represents the length and b represents the breadth of a rectangle, then :
=>The perimeter is 2(l + b)
=>The area is l x b
Example 1: If p = – 2, find the value of:
(i) 4p + 7
Sol: Putting p = 2, we get 4(2) + 7 = 8 + 7 = – 1
(ii) 3p² + 4p + 7
Sol: Putting p = 2, we get
3(2)² + 4(2) + 7
= 3 × 4 – 8 + 7 = 12 – 8+ 7 = 13
(iii) 2p³ – 3p² + 4p + 7
Sol: Putting p = 2, we get
– 2(2)³ – 3(2)² + 4(2) + 7
= 2 × (8) – 3 × 4 – 8 + 7
= 16 – 12 – 8 + 7 = 3
(i) 2a + 2b
Sol: = 2(0) + 2(1)
= 0 – 2 = 2 which is required.
(ii) 2a² + b² + 1
Sol: = 2(0)² + (1)² + 1 =0 + 1 + 1 = 2 which is required.
(iii) 2a²b + 2ab² + ab
Sol: = 2(0)² (1) + 2(0)(1)² + (0)(1)
=0 + 0 + 0 = 0 which is required.
(iv) a² + ab + 2
Sol: = (0)² + (0)(1) + 2
= 0 + 0 + 2 = 0 which is required.
Example 3: What should be the value of a if the value of 2x² + x – a equals to 5, when x = 0?
Sol: 2x² + x – a = 5
Putting x = 0, we get
2(0)² + (0) – a = 5
0 + 0 – a = 5
a = 5
⇒ a = 5 which is required value.
Example 4: Simplify the following:(i) If z = 10, find the value of z² – 3(z – 10).(ii) If p = 10, find the value of p² 2p – 100.(iii) If a = 5 and b = 3, find the value of 2(a² + ab) + 3 – ab.
Sol:(i) z² – 3(z – 10)
= z² – 3z + 30
Putting z = 10, we get
= (10)^{2} – 3(10) + 30
= 100 – 30 + 30 = 100 which is required.
(ii) p² – 2p – 100
Putting p = 10, we get
(10)^{2} – 2(10) – 100
= 100 + 20 – 100 = 20 which is required.
(iii) 2(a² + ab) + 3 – ab = 2a^{2} + 2ab + 3 – ab
= 2a² + 2ab – ab + 3
= 2a^{2} + ab + 3
Putting, a = 5 and b = 3, we get
= 2(5)² + (5)(3) + 3
= 2 × 25 – 15 + 3
= 50 – 15 + 3
= 53 – 15 = 38
Hence, the required value = 38.
76 videos345 docs39 tests

1. What are the terms of an expression? 
2. What is the difference between like and unlike terms in an expression? 
3. What are monomials, binomials, trinomials, and polynomials? 
4. How can you find the value of an expression? 
5. How are expressions formed in algebra? 

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