Simplified form of the algebraix expression $(0.5 u^{3} - u^{2}) (0.5 u^{3} - u^{2}) =$ $u^{6} - u^{5} +$

0.25

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u^{4}

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1

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u^{3}

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Solution

The correct option is B $u^{4}$
Given $(0.5 u^{3} - u^{2}) (0.5 u^{3} - u^{2})$

$= (\frac{1}{2} u^{3} - u^{2}) (\frac{1}{2} u^{3} - u^{2})$
$∴$ Using FOIL, $(\frac{1}{2} u^{3} - u^{2}) (\frac{1}{2} u^{3} - u^{2})$
$= \frac{1}{2} u^{3} \times \frac{1}{2} u^{3} - \frac{1}{2} u^{3} \times u^{2} - u^{2} \times \frac{1}{2} u^{3} + u^{2} \times u^{2}$

$= \frac{1}{4} u^{6} - u^{5} + u^{4}$
$= 0.25 \times u^{6} - u^{5} + u^{4}$

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