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Solve 38x2yz2/-19xy2z3

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  • Last Updated : 16 Jan, 2022
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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

Based on the number of terms present in algebraic expression, they are divided into majorly three types. Let’s take a look at them in detail,

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

Some other types of expression 

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

Some algebraic Formulae

(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) 

Solve 38x2yz2/-19xy2z3

Solution: 

= {38x2yz2}/{-19xy2z3}

Divide like terms 

= -(38 / 19) × (x2 / x ) × (y / y2 ) × ( z2 / z3 )

By simplifying 

= – 2x / yz

So the final result is – 2x / yz

Similar Problems 

Question 1: 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)

Question 2:  Solve for x: 6x – 50 = x + 3x

Solution:

6x – 50 = x + 3x

6x – 50 = 4x

6x – 4x = 50

2x = 50

x = 50/2

x = 25

Question 3: Find out the constant from the following algebraic expressions,

  1. x3 + 3x2 – 8
  2. 4 + y5

Answer:

Constants are the terms that do not have any variable.

Therefore, in the first term -8 is the constant and in the second term 4 is the constant.

Question 4: Simplify (4x – 5) – (5x + 1)

Solution:

Given that, (4x – 5) – (5x + 1)

  • Step 1: Remove parentheses and apply the signs carefully.

= 4x – 5 – 5x – 1

  • Step 2: Bring like terms together

= 4x – 5x – 5 – 1

  • Step 3: Now add or subtract the like terms

= -x – 6

= -(x + 6)

So the final result is -(x + 6)

Question 5 : Factorize 6a(a + 6)2/3 + 8(a + 6)1/3

Solution:

Given [6a(a + 6)2/3] + [8(a + 6)1/3]

From above expression we will factorize

= [2.3a(a + 6)2/3] + [(2)3 (a + 6)1/3]

= 2(a + 6)1/3 [{3a(a + 6)1/3 + 22]

=  2(a + 6)1/3 {3a(a + 6)1/3 + 4}

=  2(a + 6)1/3 {3a(a + 6)1/3 + 4}

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