Advertisements
Advertisements
Question
Write the following cube in expanded form:
`[x-2/3y]^3`
Advertisements
Solution
(x - y)3 = x3 - y3 - 3xy(x - y)
Using Identity
`[x - 2/3y]^3 = x^3 - (2/3y)^3 - 3(x)(2/3y)(x - 2/3y)`
= `x^3 - 8/27y^3 - 2xy(x - 2/3y)`
= `x^3 - 8/27y^3 - 2x^2y + 4/3xy^2`
APPEARS IN
RELATED QUESTIONS
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Evaluate of the following:
(598)3
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
If x = −2 and y = 1, by using an identity find the value of the following
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If x + y = 9, xy = 20
find: x2 - y2.
If p + q = 8 and p - q = 4, find:
pq
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Simplify:
(2x + y)(4x2 - 2xy + y2)
Expand the following:
(3a – 5b – c)2
