Expand the algebraic expression $x^{2} (x^{3} - 3 x^{2} - 4)$

x^{5} - 3 x^{4} - 4 x^{2}

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x^{5} + 3 x^{4} - 4 x^{2}

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x^{5} - 3 x^{4} + 4 x^{2}

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x^{5} - 3 x^{3} - 4 x^{2}

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Solution

The correct option is A $x^{5} - 3 x^{4} - 4 x^{2}$
$x^{2} (x^{3} - 3 x^{2} - 4)$
Using Distributive property of multiplication,
$x^{2} (x^{3} - 3 x^{2} - 4) = x^{2} \cdot x^{3} - 3 x^{2} \cdot x^{2} - 4 x^{2}$
Applying laws of exponents,
$x^{2 + 3} - 3 x^{2 + 2} - 4 x^{2}$
$= x^{5} - 3 x^{4} - 4 x^{2}$

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