Advertisement Remove all ads

If X = −2 and Y = 1, by Using an Identity Find the Value of the Following ( 5 Y + 15 Y ) ( 25 Y 2 − 75 + 225 Y 2 ) - Mathematics

Answer in Brief

If x = −2 and y = 1, by using an identity find the value of the following

\[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]
Advertisement Remove all ads

Solution

Given \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]

We shall use the identity `a^3 + b^3 = (a+b)(a^2 - ab + b^2)`,

We can rearrange the  \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]as

` = (5y + 15/y)[(5y)^2 + (15/y)^2 - (5y) (15/y)]`

` = (5y)^3 + (15/y)^3`

 ` = (5y) xx (5y) xx (5y) + (15/y) xx (15/y) xx (15/y)`

` = 125y^3 + 3375/y^3`

Now substituting the value  y = 1in  `125y^3 + 3375/y^3`

` = 125y^3 + 3375/y^3`

 `= 125(1)^3 + 3375/(1)^3` 

`= 125 + 3375` 

` = 3500`

Hence the Product value of  \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]is  3500.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.4 | Q 6.3 | Page 25
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×