Advertisements
Advertisements
प्रश्न
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Advertisements
उत्तर
Given \[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
We shall use the identity `(a-b)(a^2 + ab+ b^2) = a^3 - b^3`
We can rearrange the ` (3/5 - 5/y) (9^2/x^2 + 25/y^2 + 15/(xy))`as
` = ((3/x - 5/y) ((3/x)^2 + (5/y)^2 + (3/x)(5/y))`
` = (3/x)^3 - (5/y)^3 `
\[= \left( \frac{3}{x} \right) \times \left( \frac{3}{x} \right) \times \left( \frac{3}{x} \right) - \left( \frac{5}{y} \right) \times \left( \frac{5}{y} \right) \times \left( \frac{5}{y} \right)\]
\[ = \frac{27}{x^3} - \frac{125}{y^3}\]
Hence the Product value of `(3/x - 5/y) (9^2/x^2 + 25/y^3 + 15/(xy))`is `27/x^3 - 125/y^3`.
APPEARS IN
संबंधित प्रश्न
Write the following cube in expanded form:
(2a – 3b)3
Evaluate the following using suitable identity:
(102)3
Evaluate the following using suitable identity:
(998)3
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Write in the expand form: `(2x - y + z)^2`
Evaluate the following:
(98)3
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
The product (x2−1) (x4 + x2 + 1) is equal to
If a + b = 7 and ab = 10; find a - b.
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
Simplify:
(x + y - z)2 + (x - y + z)2
Using suitable identity, evaluate the following:
1033
Expand the following:
(–x + 2y – 3z)2
