Question

help me plzzz anyone? plz give ans in pic

Answer 1

Hey mate!

Here's ur answer dear:-)
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Let's see ur answer...

Let f ( a ) = (a+b+c)^3 - (a^3+b^3+c^3)

put a = -b in f(x) , we get

f(-b) = (-b + b +c ) ^3-[(-b)^3+b^3+c^3)]

f(-b) = c^3 - [ -b^3+ b^3 c^3]

f(-b) = c^3 - c^3

•°• f (-b) = 0

Hence, (a+b) is a factor of [(a+b+c)^3-(a^3+b^3+c^3)].

Similarly, we can prove (b+c) and (c+a) are factors of [(a+b+c)^3 - (a^3+b^3+c^3)]

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HOPE IT HELPS!

☺☺☺

Answer 2

Hey mate!

Here is yr answer.......


Given,

=> (a+b+c)³ - (a³+b³+c³)


Let f(a) = (a+b+c)³ - (a³+b³+c³)

a +b = 0
a = -b

f(-b) = (-b+b+c)³ - (-b³+b³+c³)

f(-b) = (c)³ - c³

f(-b) = 0

Since, f(-b) = 0 ...

a+b is the zero of the polynomial or factor of the polynomial


Now,


f(b) = (a+b+c)³ - (a³+b³+c³)

b+c = 0
b = -c

f(-c) = (a-c+c)³ - (a³-c³+c³)

f(-c) = (a)³ - a³

f(-c) = 0

since, f(-c) = 0

Therefore, b+c is the factor of the polynomial!


And,


f(c) = (a+b+c)³ - (a³+b³+c³)

c+a = 0
c = -a


f(-a) = (a+b-a)³ - (a³+b³-a³)

f(-a) = (b)³ - b³

f(-a) = 0


since, f(-a) = 0

Therefore, c+a is the factor of the polynomial!


Hence, a+b , b+c , c+a are the factors of the polynomial (a+b+c)³ - (a³+b³+c³)


Hope it helps....


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