Advertisements
Advertisements
Question
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
Advertisements
Solution
We have
`(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
`=[x^2 + y^2 + (-z)^2]^2 - [x^2 + (-y^2) + (z^2)]^2`
`= [(x^2)^2 + (y^2)^2 + (-z^2)^2 + 2(x^2)(y^2) + 2(y^2)(-z^2) + 2(x^2)(-z^2)]`
`-[(x^2)^2 + (-y^2)^2 + (z^2)^2 + 2(x^2)(-y^2) + 2(-y^2)z62 + 2x^2z^2]`
`[∵ (a + b + c)^2 = a^2 + b^2 = c^2 + 2ab + 2bc + 2ca]`
`= x^4 + y^2 + z^4 + 2x^2y^2 - 2z^2x^2 - x^4 - y^4 - z^4 + 2x^2y^2 + 2y^2z^2 - 2z^2x^2`
`= 4x^2y^2 - 4z^2x^2`
`∴ (x^2 + y^2 - z^2)^2 - (x^2 - y^2 + z^2)^2 = 4x^2y^2 - 4z^2x^2`
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
104 × 96
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Write in the expanded form:
(2a - 3b - c)2
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate of the following:
1113 − 893
Simplify of the following:
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
Use the direct method to evaluate :
(2a+3) (2a−3)
Evaluate: (9 − y) (7 + y)
Expand the following:
(m + 8) (m - 7)
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If x + y = 9, xy = 20
find: x - y
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If p + q = 8 and p - q = 4, find:
pq
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Which one of the following is a polynomial?
Expand the following:
(4a – b + 2c)2
