The fourth term from end in expansion of $(x^{2} - 2 y^{3})^{4}$ .

8 x^{3} y^{4}

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- 8 x^{6} y^{3}

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45 x^{2} y^{4}

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36 x^{2} y^{2}

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Solution

The correct option is B $- 8 x^{6} y^{3}$
To find fourth term from end of ${(x^{2} - 2 y^{3})}^{4}$ we find fourth term from begining of ${(- 2 y^{3} + x^{2})}^{4}$
$T_{3 + 1}$ = $^{4} C_{3} . (- 2)^{4 - 3}$ $y^{3}$ . $x^{6}$
$T_{4}$ = $4. (- 2) y^{3} . x^{6}$
$T_{4}$ = -8. $x^{6} . y^{3}$

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