Question

Factorize: 4x cube -81x​

Answer 1

Answer:

$4 {x}^{3} - 81x = 4x( {x}^{2} - \frac{81}{4} ) \\ = (4x)( {x}^{2} - \frac{ {9}^{2} }{ {2}^{2} } ) \\ = (4x)(x - \frac{9}{2} )(x + \frac{9}{2} ) \\ by \: using \: formula \: {x}^{2} - {y}^{2} = (x + y)(x - y) \\ hence \: if \: we \: hve \: to \: find \: its \: zeroes \: then \: put \: \\ 4x = 0 \\ and \: (x - \frac{9}{2} ) = 0 \\ and \: (x + \frac{9}{2} ) = 0 \\ and \: you \: will \: get \: \\ x = 0 \: \: \: or \: \: \: \: \: \frac{9}{2} \: \: \: \: or \: \: \: \: - \frac{9}{2}$

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