Advertisements
Advertisements
प्रश्न
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Advertisements
उत्तर
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
= `(-sqrt2x)^2 + (y)^2 + (2sqrt2z)^2 + 2(-sqrt2x)(y) + 2(y)(2sqrt2z) + 2(-sqrt2x)(2sqrt2z)`
= `(-sqrt2x + y + 2sqrt2z)^2`
= `(-sqrt2x + y + 2sqrt2z)(-sqrt2x + y + 2sqrt2z)`
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
If a − b = 4 and ab = 21, find the value of a3 −b3
Evaluate of the following:
(103)3
Simplify of the following:
(x+3)3 + (x−3)3
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
If a − b = 5 and ab = 12, find the value of a2 + b2
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Find the square of `(3a)/(2b) - (2b)/(3a)`.
Use the direct method to evaluate :
(4+5x) (4−5x)
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Factorise the following:
9y2 – 66yz + 121z2
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
