Advertisements
Advertisements
Question
Expand the following:
`(1/x + y/3)^3`
Advertisements
Solution
`(1/x + y/3)^3 = (1/x)^3 + (y/3)^3 + 3(1/x)(y/3)(1/x + y/3)` ...[Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)]
= `1/x^3 + y^3/27 + y/x(1/x + y/3)`
= `1/x^3 + y^3/27 + y/x^2 + y^2/(3x)`
APPEARS IN
RELATED QUESTIONS
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Factorise:
27x3 + y3 + z3 – 9xyz
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Simplify (2x + p - c)2 - (2x - p + c)2
Evaluate of the following:
(598)3
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Use identities to evaluate : (101)2
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Evaluate: (9 − y) (7 + y)
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
