Advertisements
Advertisements
Question
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Advertisements
Solution
We have,
`[x^2 - x + 1]^2 - [x^2 + x + 1]^2`
`= [(x^2)^2 + (-x)^2 + 1^2 + 2(x^2)(-x) + 2(-x)(1) + 2x^2 (1)] - [(x^2)^2 + (x)^2 + (1)^2 + 2x^2 (x) + 2(x)(1) + 2(x^2)(1)]`
`= x^4 + x^2 + 1 - 2x^3 - 2x + 2x^2 - x^2 - x^4 - 1 - 2x^3 - 2x - 2x^2`
`[∵ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca]`
`= -4x^3 - 4x`
`= -4x [x^2 + 1]`
`∴ [x^2 - x + 1]^2 - [x^2 + x + 1]^2 = -4x[x^2 + 1]`
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Evaluate of the following:
1043 + 963
Find the following product:
If x = −2 and y = 1, by using an identity find the value of the following
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
Use identities to evaluate : (502)2
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Find the squares of the following:
9m - 2n
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If x + y = 9, xy = 20
find: x2 - y2.
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
