Advertisements
Advertisements
Question
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Solution
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
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
Write the following cube in expanded form:
(2x + 1)3
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Evaluate the following using identities:
117 x 83
Write in the expanded form:
`(m + 2n - 5p)^2`
Write in the expanded form: (-2x + 3y + 2z)2
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If a − b = 4 and ab = 21, find the value of a3 −b3
Evaluate of the following:
463+343
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
Evaluate:
483 − 303 − 183
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
If 3x + 4y = 16 and xy = 4; find the value of 9x2 + 16y2.
Factorise the following:
4x2 + 20x + 25
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
