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**12. Algebraic Expressions**

**Understanding Algebraic Expressions**

Expressions that contain **only constants **are called **numeric or arithmetic expressions.**

Expressions that contain **only constants** are called **numeric or arithmetic expressions.** Expressions that contain **constants **and** variables**, or** just variables**, are called **algebraic expressions**.

While writing algebraic expressions, we do not write the **sign of multiplication**. An algebraic expression containing only variables also has the constant 1 associated with it. The parts of an algebraic expression joined together by plus (+) signs are called its **terms**. A term that contains variables is called a** variable term.**

A term that contains only a number is called a** constant term. **The constants and the variables whose product makes a term of an algebraic expression, are called the** factors of the term**. The factors of a constant term in an algebraic expression are not considered. The numerical factor of a variable term is called its **coefficient**. The variable factors of a term are called its **algebraic factors.**

Terms that have** different algebraic factors** are called **unlike terms**. Terms that have the** same algebraic factors are called like terms**. 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**. All algebraic expressions that have one or more terms are called polynomials. Therefore, binomials and trinomials are also** polynomials.**

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**Operations on Algebraic Expressions**

We can perform** arithmetic operations on algebraic expressions**. To **add the like** terms in an** **algebraic expression...

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 together.** 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.

Thererfore,

= (4 + 8) x + 3

= 12x + 3

**Unlike terms** remain** unchanged i**n the sum or difference of algebraic expressions.

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**Application of Algebraic Expressions**

Algebraic expressions can be used to represent **number patterns.**

Algebraic expressions can be used to represent** number patterns**. In the following example, we can find the relation between number of 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.

In a similar way, we can write **formulas** for the perimeter and area for **different geometrical figures** using simple, easy-to-remember algebraic expressions

**â€¢ **If s represents the side of a** square**, then its:

o Perimeter is **4s**

o Area is **s ^{2}**

**â€¢ ** If l represents the length and b represents the breadth of a rectangle, then its:Perimeter is 2(l + b) Area is l x b

211 videos|109 docs|45 tests

### NCERT Solutions(Part - 2) - Algebraic Expressions

- Doc | 6 pages
### Test: Algebraic Expressions - 1

- Test | 10 ques | 10 min
### Examples: Addition of Algebraic Expressions

- Video | 05:11 min
### Subtraction of Algebraic Expressions

- Video | 05:24 min
### Test: Algebraic Expressions - 2

- Test | 20 ques | 20 min

- NCERT Textbook - Algebraic Expressions
- Doc | 20 pages
- NCERT Solutions(Part - 1) - Algebraic Expressions
- Doc | 13 pages