Note the following cube root calculations
The cube root of the first term x3 = x ← This is {a}The cube root of the second term 27y9 = 3y3 ← This is {b}
Since both cube roots are integer constants and powers, x3 - 27y9 is in the Difference of cubes format
The formula for factoring the Difference of cubes is as follows:
a3 - b3 = (a - b)(a2 + ab + b2)Calculate ab
ab = (x)(3y3)ab = (1 x 3)xy3
ab = 3xy3
Calculate the square of the a term:
The square of the a term = (x)2 = x(1 x 2)The square of the a term = (x)2 = x2
Calculate the square of the b term:
The square of the b term = (3y3)2 = 32y(3 x 2)The square of the b term = (3y3)2 = 9y6
Our factored expression using the Difference of cubes formula becomes:
(x - 3y3)(x2 + 3xy3 + 9y6)Our factored out term becomes:
(x - 3y3)(x2 + 3xy3 + 9y6)
