# Divide and simplify (21×3 – 7)/(3x – 1)

The basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are termed here as variables. this expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is termed a coefficient.

An idea of expressing numbers using letters or alphabets without specifying their actual values is termed an** algebraic expression.**

**What is an Algebraic Expression?**

In mathematics, It is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. these Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as An algebraic expression (or) a variable expression.

Examples: 2x + 4y – 7, 3x – 10, etc.

The above expressions are represented with the help of unknown variables, constants, and coefficients. The combination of these three terms is termed as an expression. unlike the algebraic equation, It has no sides or ‘equals to’ sign.

**Types of Algebraic expression**

- Monomial Expression
- Binomial Expression
- Polynomial Expression

**Monomial Expression**

An expression that has only one term is termed a Monomial expression.

Examples of monomial expressions include 4x^{4}, 2xy, 2x, 8y, etc.

**Binomial Expression**

An algebraic expression which is having two terms and unlike are termed as a binomial expression

Examples of binomial include 4xy + 8, xyz + x^{2}, etc.

**Polynomial Expression**

An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression.

Examples of polynomial expression include ax + by + ca, x^{3}+ 5x + 3, etc.

**Some Other Types of Expression**

We have other expressions also apart from monomial, binomial, and polynomial types of expressions which are

- Numeric Expression
- Variable Expression

**Numeric Expression**

An expression that consists of only numbers and operations, but never includes any variable is termed a numeric expression.

Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.

**Variable Expression**

An expression that contains variables along with numbers and operations to define an expression is termed as A variable expression.

Some examples of a variable expression include 5x + y, 4ab + 33, etc.

**Some algebraic formulas**

(a + b)

^{2}= a^{2}+ 2ab + b^{2}(a – b)

^{2}= a^{2}– 2ab + b^{2}(a + b)(a – b) = a

^{2}– b^{2}(x + a)(x + b) = x

^{2}+ x(a + b) + ab(a + b)

^{3}= a^{3}+ b^{3}+ 3ab(a + b)(a – b)

^{3}= a^{3}– b^{3}– 3ab(a – b)a

^{3}– b^{3}= (a – b)(a^{2}+ ab + b^{2})a

^{3}+ b^{3 }= (a + b)(a^{2 }– ab + b^{2})

There are some terms of algebraic expression which basically used

examples of using these terms

**If 2x ^{2}+3xy+4x+7 is an algebraic expression.**

Then, 2x^{2}, 3xy, 4x, and 7 are the Terms

Coefficient of term:2 is the coefficient of x^{2}

Constant term:7

Variables:here x, y are variables

Factors of a term:If 2xy is a term, then its factors are 2, x, and y.

Like and Unlike terms :Example of like and unlike terms:

Like terms: 4x and 3xUnlike terms: 2x and 4y

### Divide and simplify (21x^{3} – 7)/(3x – 1)

**Solution:**

(21x

^{3}– 7)/(3x – 1)= [7 (3x

^{3}– 1)] / (3x-1)= [7 {(3x)

^{3}– (1)^{3}] / ( 3x-1)= [7 (3x-1)(9x

^{2}+1 + 3x)] / (3x-1) { a^{3}– b^{3}= (a – b)(a^{2 }+ ab + b^{2}) }= 7 (9x

^{2}+1 + 3x)= 63x

^{2}+ 7 + 21x

**Similar Questions**

**Question 1: Simplify (3x – 5) – (5x + 1).**

**Solution:**

We have

(3x – 5) – (5x + 1)

= 3x – 5 – 5x – 1

= -2x -6

= -2 (x + 3)

**Question 2: Find out the constant from the following algebraic expressions,**

**x ^{3} + 3x^{2} – 6**

**5 + y ^{5}**

**Answer:**

Constants are the terms that do not have any variable,

therefore, in the first term -6 is the constant and in the second term 5 is the constant.

**Question 3: Simplify 4x ^{2} – 3x + 7x^{2} – 5x + 5**

**Solution:**

4x

^{2}– 3x + 7x^{2}– 5x + 5= 4x

^{2}+ 7x^{2}– 3x – 5x + 5= 11x

^{2}– 8x + 5

**Question 4: Simplify 3x + 4(x-2) = 20**

**Solution:**

we have 3x + 4(x-2) = 20

3x + 4x – 8 = 20

7x – 8 = 20

7x = 20+ 8

7x = 28

x = 28/7

x = 4

**Question 5: Solve (6 – 3w)(-w ^{2})**

**Solution:**

(6 – 3w)(-w

^{2})By simplifying

= (6 – 3w)(-w

^{2})= [6 × (-w

^{2})] – [3w × -(w^{2})]= -6w

^{2}– (-3w^{3})= -6w

^{2}+ 3w^{3}= 3w

^{2}(-2 + w)= 3w

^{2 }(w – 2)

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