Statement-1 (A): a^3+b^3+3 a b-1=(a+b-1) (a^2+b^2+a+b-a b+1 ) Sta… - Vidyadip

MCQ

Statement-1 (A): $a^3+b^3+3 a b-1=(a+b-1)\left(a^2+b^2+a+b-a b+1\right)$
Statement-2 (R): $ a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2+a b+b c+c a\right)$

A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
✓
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.

✓

Answer

Correct option: C.

Statement-1 is True, Statement-2 is False.

(c)
Statement-2 is not true, because
$a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
Using this formula, we obtain
$a^3+b^3+(-1)^3-3 a b(-1)=(a+b+(-1))\left(a^2+b^2+(-1)^2-a b-a(-1)-b(-1)\right)$
$\Rightarrow \quad a^3+b^3+3 a b-1=(a+b-1)\left(a^2+b^2+a+b-a b+1\right)$
So, statement-1 is true. Hence, option (c) is correct.

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