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Simplify (3x – 5) – (5x + 1)

  • Last Updated : 16 Jan, 2022

Algebra is the branch of mathematics that contains numerals and variables with operators. Or we can say that 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.

Algebraic Expression

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

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 is equal to the sign. For example, 4x + 7 is a term in which:

  • x is a variable with an unknown value and can take any value.
  • 4 is known as the coefficient of x and a constant value that is used with the variable term that is x.
  • 7 is the constant value.

Types of Algebraic expression

  1. Monomial Expression: An expression that has only one term is termed a Monomial expression. Examples are 4x4, 2xy, 2x, 8y, etc.
  2. Binomial Expression: An algebraic expression which is having two terms and unlike are termed as the binomial expression. Examples are 4xy + 8, xyz + x2, etc.
  3. Polynomial Expression: An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression. Examples are px + qy + rp, x3 + 9x + 3, etc.

Some other types of expression are:

  1. Numeric Expression: An expression consisting of only numbers and operations, but never containing any variable is termed a numeric expression. Some of the examples are 11 + 5, 14 ÷ 2, etc.
  2. Variable Expression: An expression that contains variables along with numbers and operations to define an expression is termed a variable expression. Some examples are 5x + y, 4ab + 33, etc.

Algebraic Formula

Some algebraic formulas we have:

  • (x + y)2 = x2 + 2xy + y2
  • (x – y)2 = x2 – 2xy + y2
  • (x + y)(x – y) = x2 – y2
  • (x + y)3 = x3 + y3 + 3xy(x + y)
  • (x – y)3 = x3 – y3 – 3xy(x – y)
  • x3 – y3 = (x – y)(x2 + xy + y2)
  • x3 + y3 = (x + y)(x2 – xy + y2)

Simplify (3x – 5) – (5x + 1)

Solution:

Given that (3x – 5) – (5x + 1)

Step 1: Remove parentheses and apply the signs carefully.

 =  3x – 5 – 5x – 1

Step 2: Bring like terms together

= 3x – 5x – 5 – 1

Step 3: Now add or subtract the like terms

= -2x – 6

= -2(x + 3)

So the final result is -2(x + 3)

Similar Question  

Question 1: Simplify the expression: (8 – 2w)(-w2).

Solution:

Given that (8 – 2w)(-w2)

By simplifying, we get

= (8 – 2w)(-w2)

= [8 x (-w2)] – [(2w) x -(w2)]

=  -8w2 – (- 2w3)

= -8w2 + 2w3

=  2w2(-4 + w)

= 2w2(w – 4)

Question 2: Simplify the expression: 5x2 – 3x + 7x2 – 4x + 9.

Solution:

Given that 5x2 – 3x + 7x2 – 4x + 9

By simplifying, we get

=  5x2 + 7x2 – 3x -4x + 9 

= 12x2 – 7x + 9 

Question 3: Divide and simplify: (21x3 – 7)/(3x – 1).

Solution:  

Given that (21x3 – 7)/(3x – 1)

= [7(3x3 – 1)] / (3x – 1)

= [7((3x)3 – (1)3)] / (3x – 1)

By using identity a3 – b3 = (a – b)(a2 + ab + b2) we get,

= [7((3x – 1)(9x2 + 1 + 3x))] / (3x – 1)               

= 7(9x2 + 1 + 3x)

= 63x2 + 7 + 21x

Question 4: Simplify 3x + 2(x – 2) = 21.

Solution: 

We have 3x + 2(x – 2) = 21

3x + 2x – 4 = 21

5x – 4 = 21

5x = 21 + 4

5x = 25

x = 25/5

x = 5

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