Advertisements
Advertisements
Question
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Advertisements
Solution
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
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Write the following cube in expanded form:
(2x + 1)3
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Write in the expanded form (a2 + b2 + c2 )2
Simplify (a + b + c)2 + (a - b + c)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^2 - x + 1)^2 - (x^2 + x + 1)^2`
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Evaluate of the following:
463+343
Evaluate of the following:
1043 + 963
Evaluate of the following:
933 − 1073
Evaluate:
253 − 753 + 503
Evaluate:
483 − 303 − 183
If a2 + b2 + c2 − ab − bc − ca =0, then
Find the square of 2a + b.
Use identities to evaluate : (998)2
Use the direct method to evaluate :
(xy+4) (xy−4)
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
