Question : If $a + b + c$ = 6 and $a b + b c + c a$ = 11, then the value of $b c (b + c) + c a (c + a) + a b (a + b) + 3 a b c$ is:
Option 1: 33
Option 2: 66
Option 3: 55
Option 4: 23

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Question : What is the value of $a^{3} + b^{3} + c^{3}$ if $(a + b + c) = 0$ ?

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Answer 1

Correct Answer: 66

Solution : Given: $a + b + c$ = 6 and $a b + b c + c a$ = 11
To find:
$b c (b + c) + c a (c + a) + a b (a + b) + 3 a b c$
= $b^{2} c + b c^{2} + c^{2} a + c a^{2} + a^{2} b + a b^{2} + a b c + a b c + a b c$
= $b c (a + b + c) + a c (a + b + c) + a b (a + b + c)$
= $(a + b + c) (a b + b c + a c)$
Putting the values, we get
⇒ 6 $\times$ 11 = 66
Hence, the correct answer is 66.

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Question : If a+b+c = 6 and ab+bc+ca = 11, then the value of bc(b+c)+ca(c+a)+ab(a+b)+3abc is:Option 1: 33Option 2: 66Option 3: 55Option 4: 23

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Question : If $a + b + c$ = 6 and $a b + b c + c a$ = 11, then the value of $b c (b + c) + c a (c + a) + a b (a + b) + 3 a b c$ is:
Option 1: 33
Option 2: 66
Option 3: 55
Option 4: 23