# CLASS-8DIVISION BY MONOMIAL BY MONOMIAL

Division of a Monomial by a Monomial –

To divide one monomial by another, divide the numerical coefficient of the dividend by the numerical coefficient of the divisor and the powers of variables in the dividend by the corresponding powers in the divisor. Then multiply all the quotients.

Quotient of two monomials = (quotient of numerical factors) X (quotient of literal factors)

There are some example are given below for your better understanding -

Example.1) Divide 24x²y⁵ by 8xy

Ans.)   As per the given condition, we have to  24x²y⁵ ÷ 8xy

24x²y⁵          24

So, 24x²y⁵ ÷ 8xy = ---------- = -------- x²⁻¹ y⁵⁻¹ =  3 xy⁴   (Ans.)

8xy             8

Example.2)  Divide 36a⁴b⁸c²d⁶ by 9a⁵bᶟc²d²

Ans.) As per the given condition, we have to 36a⁴b⁸c²d⁶ ÷ 9a⁵bᶟc²d²

36a⁴b⁸c²d⁶ ÷ 9a⁵bᶟc²d²

36a⁴b⁸c⁵d⁶         36         a⁴         b⁸          c²          d⁶

= ------------- = ------ X ------ X ------ X ------- X -------

9a⁵bᶟc²d²          9          a⁵         bᶟ          c²

=  4 a⁴⁻⁵ b⁸⁻c²⁻² d⁶⁻²

= 4 a⁻¹ b⁵ c⁰ d⁴  =  4 a⁻¹ b⁵ . 1 . d⁴

= 4 a⁻¹ b⁵ d⁴

4 b⁵ d⁴

= ------------               (Ans.

a

Example.3) Divide 30x⁴y² + 15 x²y²- 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ by  5 x⁴y⁶

Ans.) As per the given condition we have to  30x⁴y²+ 15 x²y²- 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ ÷ 5 x⁴y⁶

30x⁴y²+ 15 x²y² - 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ ÷ 5 x⁴y⁶

30x⁴y² + 15 x²y² - 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵

=  ------------------------------------------------

5 x⁴y⁶

30x⁴y²       15 x²y²       20 x⁵y⁴        10 x⁵y⁶          25 x⁸y⁵

= --------- + --------- - ---------- + ---------- - -----------

5 x⁴y⁶        5 x⁴y⁶          5 x⁴y⁶         5 x⁴y⁶           5 x⁴y⁶

=  6 x⁴⁻⁴. y²⁻⁶ + 3 x²⁻⁴. y²⁻⁶ - 4 x⁵⁻⁴ y⁴⁻⁶ + 2 x⁵⁻⁴ y⁶⁻⁶ - 5 x⁸⁻⁴ y⁵⁻⁶

=  6 x⁰ y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x¹ y⁻² + 2x¹ y⁰ - 5x⁴ y⁻¹

= 6.1. y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x y⁻² + 2x.1 - 5x⁴ y⁻¹

=  6 y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x y⁻² + 2x - 5x⁴ y⁻¹

6             3             4x                  5x⁴

= -------- + -------- - --------- + 2x - ---------      (Ans.)

y⁴          x² y⁴           y²                   y