Question

Find the product(a-b-c)(a2+b2+c2+ab-bc+ca)

Answer 1

(a-b-c)(a2+b2+c2+ab-bc+ca) =a3+ab2+ac2+a2b-abc+a2c-a2b-b3-bc2-ab2-b2c-abc-a2c-cb2-c3-abc-bc2-c2a=a3-b3-c3-2bc2-2b2c-3abc

Answer 2

Answer:

(a-b-c)(a²+b²+c²+ab-bc+ca)

=a³-b³-c³-3abc

Step-by-step explanation:

we know the algebraic identity:

(x+y+z)(x²+y²+z²-xy-yz-zx)

=x³+y³+z³-3xyz--(1)

Now,

we have ,

(a-b-c)(a²+b²+c²+ab-bc+ca)

=[a+(-b)+(-c)][a²+(-b)²+(-c)²-a(-b)-(-b)(-c)-(-c)a]

= a³+(-b)³+(-c)³-3a(-b)(-c)

= a³-b³-c³-3abc /* From (1)

Therefore,

(a-b-c)(a²+b²+c²+ab-bc+ca)

=a³-b³-c³-3abc

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