Advertisements
Advertisements
Question
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Advertisements
Solution
We have,
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
`=[x^2 + y^2 + (-2z)^2 + 2xy + 2(y)(-2z)] - x^2 - y^2 - 3z^2 + 4xy`
`= x^2 + y^2 + 4z^2 + 2xy - 4yz - x^2 - y^2 - 3z^2 = 4xy`
`= z^2 + 6xy - 4yz - 4zx`
`∴ (x + y - 2z)^2 - x^2 - y^2 - 3z^2 + 4xy = z^2 + 6xy - 4yz - 4zx`
APPEARS IN
RELATED QUESTIONS
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Evaluate:
253 − 753 + 503
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
If a − b = −8 and ab = −12, then a3 − b3 =
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Find the following product:
(x2 – 1)(x4 + x2 + 1)
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
