Find the degree of the polynomial $4 a^{4} - 2 (3 + a^{4} - a b + 4 b^{3}) - 2 a^{4}$ .

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Solution

The correct option is D 3
At first glance while looking at the expression $4 a^{4} - 2 (3 + a^{4} - a b + 4 b^{3}) - 2 a^{4}$ , degree seems to be 4. But on simplification,

$4 a^{4} - 2 (3 + a^{4} - a b + 4 b^{3}) - 2 a^{4}$
$= 4 a^{4} - 6 - 2 a^{4} + 2 a b - 8 b^{3} - 2 a^{4}$
$= 2 a b - 8 b^{3} - 6$
3 would be the degree of this polynomial which is obtained from 2nd term.

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