Question

Use the sum of cubes identity to write this polynomial expression in factored form:
8x3 + 27.

Answer 1

`{8x}^(3) + 27 \\ = {8x}^(3) + {3}^(3) \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^(3) + {b}^(3) : \\ {(a + b)}^(3) = (a + b)( {a}^(2) + 2ab + {b}^(2) ) \\ {(a + b)}^(3) = ( {a}^(3) + 3{a}^(2) b + 3a {b}^(2) + {b}^(3) ) \\ ( {a}^(3) + {b}^(3) ) = {(a + b)}^(3) - 3ab(a + b) \\ \therefore( {8x}^(3) + 27) = {(8x + 3)}^(3) - 72(8x + 3)`