Advertisements
Advertisements
Question
Factorise:
27x3 + y3 + z3 – 9xyz
Advertisements
Solution
It is known that,
x3 + y3 + z3 − 3xyz = (x + y + z) (x2 + y2 + z2 − xy − yz − zx)
∴ 27x3 + y3 + z3 – 9xyz = (3x + y + z)(3x)2 + (y)2 + (z)2 – (3x)y – yz – z(3x)
= (3x + y + z)(3x)2 + y2 + z2 – 3xy – yz – 3xz
= (3x + y + z)(9x2 + y2 + z2 – 3xy – yz – 3xz)
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
`[3/2x+1]^3`
Write the following cube in expanded form:
`[x-2/3y]^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 the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate of the following:
933 − 1073
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(3b−1) (3b+1)
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate: (6 − 5xy) (6 + 5xy)
If x + y = 1 and xy = -12; find:
x - y
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Simplify:
(7a +5b)2 - (7a - 5b)2
Expand the following:
(–x + 2y – 3z)2
