State True or False:
On subtracting $a^{2} + a b + b^{2}$ from $4 a^{2} - 3 a b + 2 b^{2}$ , the answer is $3 a^{2} - 4 a b + b^{2}$ .

True

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False

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Solution

The correct option is A True
Consider $a^{2} + a b + b^{2}$ and $4 a^{2} - 3 a b + 2 b^{2}$ . Now,
$\Rightarrow 4 a^{2} - 3 a b + 2 b^{2} - (a^{2} + a b + b^{2})$
$= 4 a^{2} - 3 a b + 2 b^{2} - a^{2} - a b - b^{2}$
$= 4 a^{2} - a^{2} + 2 b^{2} - b^{2} - 3 a b - a b$
$= (4 - 1) a^{2} + (2 - 1) b^{2} + (- 3 - 1) a b$
$= 3 a^{2} + b^{2} - 4 a b$
Since, $3 a^{2} + b^{2} - 4 a b = 3 a^{2} - 4 a b + b^{2}$ , therefore, the given statement is true.

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