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 x3 + 8y3 + 6x2 y +12xy2
`3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc`
Multiply: x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3
Write the value of \[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .\]
If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =
Separate the constants and variables from the following :
`-7,7+"x",7"x"+"yz",sqrt5,sqrt("xy"),(3"yz")/8,4.5"y"-3"x",`
8 −5, 8 − 5x, 8x −5y × p and 3y2z ÷ 4x
Multiply: (2x - 3y)(2x + 3y)
Divide: 2m3n5 by - mn
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7; find the value of s.
If x = 2 and y = 3, then find the value of the following expressions
x + 1 – y
