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If $a y^{4} = {(x + b)}^{5}$ , then $5 y y_{2} =$

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${y_{1}}^{2}$

${y_{2}}^{1}$

$2 y$

$y^{2}$

answer is A.

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Detailed Solution

$a y^{4} = {(x + b)}^{5}$

$4 a y^{3} y_{1} = 5 {(x + b)}^{5}$

$4 a y^{3} y_{1} (x + b) = 5 {(x + b)}^{5}$

$4 a y^{3} y_{1} (x + b) = 5 a y^{4}$

$4 (x + b) = \frac{5 y}{y_{1}}$

$4 = \frac{y_{1} (5 y_{1}) - 5 y y_{2}}{{y_{1}}^{2}}$

$4 {y_{1}}^{2} = 5 {y_{1}}^{2} - 5 y y_{2}$

$5 y y_{2} = {y_{1}}^{2}$

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