Expand the algebraic expression $x^{3} (2 x^{4} + 4 x^{3} + 5) .$

2 x^{7} + 4 x^{6} + 5 x^{3}

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2 x^{7} + 4 x^{6} + 15 x^{3}

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2 x^{12} + 4 x^{9} + 5 x^{3}

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2 x^{12} + 4 x^{9} + 15 x^{3}

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Solution

The correct option is A $2 x^{7} + 4 x^{6} + 5 x^{3}$
$Need to simplify: - ------------------- - x^{3} (2 x^{4} + 4 x^{3} + 5)$

$x^{3} (2 x^{4} + 4 x^{3} + 5)$

Applying distributive property of multiplication: $a \times (b + c) = a \times b + a \times c$

$= x^{3} \cdot 2 x^{4} + x^{3} \cdot 4 x^{3} + x^{3} \cdot 5$

Applying the multiplication law of exponent: $a^{m} \cdot a^{n} = a^{m + n}$

$= 2 x^{3 + 4} + 4 x^{3 + 3} + 5 x^{3}$
$= 2 x^{7} + 4 x^{6} + 5 x^{3}$

$∴ x^{3} (2 x^{4} + 4 x^{3} + 5) = 2 x^{7} + 4 x^{6} + 5 x^{3} - -------------------------------------- -$

Hence, option (a.) is the correct one.

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