Advertisements
Advertisements
Question
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Advertisements
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
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Factorise the following:
64m3 – 343n3
Evaluate the following using identities:
(0.98)2
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
The product (x2−1) (x4 + x2 + 1) is equal to
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
(3b−1) (3b+1)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Evaluate: (9 − y) (7 + y)
Simplify by using formula :
(5x - 9) (5x + 9)
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If x + y = 1 and xy = -12; find:
x - y
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
