64 = 4 ^ 3
64 x ^ 3 = ( 4 x ) ^ 3
27 = 3 ^ 3
64 x ^ 3 - 27 = ( 4 x ) ^ 3 - 3 ^ 3
a ^ 3 - b ^ 3 = ( a - b ) ( a ^ 2 + a b + b ^ 2 )
In this case:
64 x ^ 3 - 27 = ( 4 x ) ^ 3 - 3 ^ 3 = ( 4 x - 3 ) * [ ( 4 x ) ^ 2 + 4 x * 3 + 3 ^ 2 ] =
( 4 x - 3 ) * ( 16 x ^ 2 + 12 x + 9 )
Factor the polynomial
64x^3-27
1 answer