Advertisements
Advertisements
प्रश्न
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Advertisements
उत्तर
We have
(a + b + c)2 + (a - b + c)2 + (a + b - c)2
`= [a^2 + b^2 + c^2 + 2ab + 2bc + 2ca] + [a^2 + b^2 + c^2 - 2bc - 2ab + 2ca] + [a^2 + b^2 + c^2 - 2ca - 2bc + 2ab]`
`[∵ (x + y + z)^2 = x^2 + y^2 + 2xy + 2yz + 2zx]`
`= 3a^2 + 3b^2 + 3c^2 + 2ab + 2bc + 2ca - 2bc - 2ab + 2ca - 2ca - 2bc + 2ab`
`= 3a^2 + 3b^2 + 3c^2 + 2ab - 2bc + 2ca`
`= 3(a^2 + b^2 + c^2) + 2(ab - bc + ca)`
`∴(a + b + c)^2 + (a - b + c)^2 + (a + b - c)^2 = 3(a^2 + b^2 + c^2) + 2[ab - bc + ca]`
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate the following using identities:
`(2x+ 1/x)^2`
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Write in the expanded form:
(2a - 3b - c)2
Write in the expanded form (a2 + b2 + c2 )2
Write in the expanded form: (ab + bc + ca)2
Write in the expanded form: (-2x + 3y + 2z)2
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Find the following product:
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
Use the direct method to evaluate :
(xy+4) (xy−4)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Expand the following:
(x - 3y - 2z)2
Simplify by using formula :
(a + b - c) (a - b + c)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
Simplify:
(7a +5b)2 - (7a - 5b)2
Expand the following:
`(1/x + y/3)^3`
