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Factorize the following expressions:

1029 – 3x^{3}

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#### Solution

= 3(343 - x^{3})

= 3(73 - x^{3})

= 3(7 - x)(7^{2} + 7 x x + x^{2}) [∵ a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2}) ]

= 3(7 - x)(49 + 7x + x^{2} )

∴ 1029 - 3x^{3} = 3(7 - x)(49 + 7x + x^{2} )

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