Advertisements
Advertisements
Question
Evaluate: (a2 + b2 + c2 - ab - bc - ca)(a + b + c)
Advertisements
Solution
(a2 + b2 + c2 - ab - bc - ca)(a + b + c)
= a (a2 + b2 + c2 - ab - bc - ca) + b (a2 + b2 + c2 - ab - bc - ca) + c (a2 + b2 + c2 - ab - bc - ca)
= a3 + ab2 + ac2 - a2b - abc - ca2 +a2b + b3 + bc2 - ab2 - b2c - abc + a2c + b2c + c3 - abc - bc2 - c2a
= a3 + b3 + c3 -a2b + a2b - ca2 + a2c + bc2 - bc2 - ab2 + ab2 - abc - abc - abc + ac2 - ac2 + b2c - b2c
= a3 + b3 + c3 - 3abc
APPEARS IN
RELATED QUESTIONS
Factorize the following expressions:
32a3 + 108b3
Factorize the following expressions:
x3y3 + 1
Find the value of the following expression: 64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]
If a + b + c = 0, then write the value of a3 + b3 + c3.
The factors of x3 − 1 + y3 + 3xy are
If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =
Evaluate: (3x - 1)(4x3 - 2x2 + 6x - 3)
Evaluate: (8 - 12x + 7x2 - 6x3)(5 - 2x)
Divide: 6x3 + 5x2 − 21x + 10 by 3x − 2
If x = 2 and y = 3, then find the value of the following expressions
2x – 3y
