Dear student,

Thanks for watching my lectures. Questions #15 and #16 are similar type of questions.

This is what we use in these two questions.

A^3-B^3=(A-B)(A^2+AB+B^2)

If you expand the righthand side of the equation, you actually get the left-hand side. Since this works for any A or B, I think it's better if we just memorize this by heart, since this pattern appears in Algebra 1, Algebra 2, and Precalculus.

Therefore, x^3-8=x^3-2^3=(x-2)(x^2+2x+4). Likewise, 8x^3-27y^3=(2x)^3-(3y)^3=(2x-3y)(4x^2+6xy+9y^2).

Thanks,

Harim Yoo