Advertisements
Advertisements
Question
Factorise the following:
27y3 + 125z3
Advertisements
Solution
We know that = (x + y) (x2 + y2 − xy) = x3 + y3
It is given that = 27y3 + 125z3 = (3y)3 + (5z)3
= (3y + 5z) [(3y)2 − (3y)(5z) + (5z)2]
= (3y + 5z) (9y2 − 15yz + 25z2)
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(3a – 7b – c)2
Evaluate the following using suitable identity:
(998)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
if `x^2 + 1/x^2 = 79` Find the value of `x + 1/x`
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Write in the expanded form: (-2x + 3y + 2z)2
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If a − b = 4 and ab = 21, find the value of a3 −b3
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
Evaluate:
253 − 753 + 503
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Simplify:
(4x + 5y)2 + (4x - 5y)2
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
