Advertisements
Advertisements
Question
If x = −2 and y = 1, by using an identity find the value of the following
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
Evaluate of the following:
(99)3
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
If a + b = 6 and ab = 20, find the value of a3 − b3
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
Use identities to evaluate : (502)2
Use the direct method to evaluate :
(4+5x) (4−5x)
Expand the following:
(2p - 3q)2
Find the squares of the following:
9m - 2n
If p + q = 8 and p - q = 4, find:
pq
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Using suitable identity, evaluate the following:
9992
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Expand the following:
(3a – 2b)3
