Factorise the expression: $32 x^{5} - 256 x^{3}$

32 x^{3} (x^{2} - 8)

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32 x^{3} (x^{2} - 16)

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32 x^{3} (x^{2} - 4)

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32 x^{3} (x^{2} - 32)

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Solution

The correct option is A $32 x^{3} (x^{2} - 8)$
$32 x^{5} - 256 x^{3} = (2 \times 2 \times 2 \times 2 \times 2 \times x^{5}) - (2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times x^{3})$

$= 2 \times 2 \times 2 \times 2 \times 2 \times x^{3} (x^{2} - 2 \times 2 \times 2 \times x^{0})$

$= 32 x^{3} (x^{2} - 8)$

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