Multiply a² + b² + c² - ab - bc - ca by a + b + c.
Answers
We have been asked to multiply a² + b² + c² - ab - bc - ca with a + b + c.
Write both of them in the parenthesis:-
= (a + b + c)(a² + b² + c² - ab - bc - ca)
We have a direct result for this expression:-
= a³ + b³ + c³ - 3abc
We can use the direct multiplication to cross-check it:-
= (a + b + c)(a² + b² + c² - ab - bc - ca)
= a³ + b²a + ac² - a²b - abc - a²c + a²b + b³ + c²b - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a
= a³ + b³ + c³ - 3abc
We get the same result as the result.
Hence, it is verified.
The product of a² + b² + c² - ab - bc - ca with a + b + c is a³ + b³ + c³ - 3abc !
Step-by-step explanation:
are identities means the algebraic equation is satisfied for each and every value of a and b. similarly for (a-b-c)^2, (a -(b+c))^2 = a^2+(b+c)^2 - 2 a(b+c) . => (a-(b+c))^2 = a^2+b^2+c^2+2ac -2ab -2ac .