Advertisements
Advertisements
Question
Factorise the following:
27y3 + 125z3
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
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Evaluate the following using suitable identity:
(102)3
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Simplify (2x + p - c)2 - (2x - p + c)2
Evaluate of the following:
463+343
If x = −2 and y = 1, by using an identity find the value of the following
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
Use identities to evaluate : (101)2
If a - b = 7 and ab = 18; find a + b.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate: (6 − 5xy) (6 + 5xy)
Expand the following:
(a + 3b)2
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Using suitable identity, evaluate the following:
9992
Factorise the following:
9y2 – 66yz + 121z2
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
