# 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

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

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

#### 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.

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#### APPEARS IN

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