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Multiplication using FOIL Rule

Simplify: 0.5...

Question

Simplify: $(0.5 u^{3} - u^{2}) (0.5 u^{3} - u^{2})$

2.5 u^{6} - u^{5} + u^{4}

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0.25 u^{6} - u^{4}

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0.25 u^{6} - u^{5} + u^{4}

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u^{6} - u^{5} + u^{4}

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Solution

The correct option is C $0.25 u^{6} - u^{5} + u^{4}$
Using the FOIL rule.
F=First terms, O= Outside terms, I = Inside terms, L= Last terms.

$(0.5 u^{3} - u^{2}) (0.5 u^{3} - u^{2})$

$= (\frac{1}{2} u^{3} - u^{2}) (\frac{1}{2} u^{3} - u^{2})$

$= \frac{1}{2} u^{3} (\frac{1}{2} u^{3} - u^{2}) - u^{2} (\frac{1}{2} u^{3} - u^{2})$

$= \frac{1}{4} u^{6} - \frac{1}{2} u^{5} - \frac{1}{2} u^{5} + u^{4}$

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

$= 0.25 u^{6} - u^{5} + u^{4}$

This is the required expression obtained using FOIL rule.
Also, we can use the identity
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$ .

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