math-algebra

Factor the polynomial

64x^3-27

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1. 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 )

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