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Factorize x^{3} -12x ( x - 4) - 64

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#### Solution

x^{3} -12x ( x - 4) - 64

= x^{3} -12x^{2} + 48x - 64

= ( x)^{3} - 3 × x^{2} × 4 + 3 × 4^{2} × x - 4^{3}

= ( x - 4)^{3 } [ ∵ a^{3} - 3a^{2}b + 3ab^{2} - b^{3} = (a - b)^{3}]

= ( x - 4)( x - 4)( x - 4)

∴ x^{3} -12x ( x - 4) - 64 = ( x - 4)( x - 4)( x - 4)

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