Hi,
Am I correct?
Express as the product of four factors.
a⁶ - b⁶
=(a - b)(a⁵ + a⁴b + ab + ab + ab⁴ + b)
Express as the product of three factors.
a⁴ - b⁴
=(a - b)(a + ab + ab + b)
Your algebra is good- it's your counting you need to work on! You don't have "four" and "three" factors.
As I believe I told you on a different forum, think of $\displaystyle (x^6- y^6)$ as $\displaystyle (x^3)^2- (y^3)^2$ and factor as the "difference of two squares", $\displaystyle (x^3+ y^3)(x^3-y^3)$. Since those are both odd powers, each will factor as you have above.
Think of $\displaystyle x^4- y^4$ as $\displaystyle (x^2)^2- (y^2)^2$. Again, you can factor that as the "difference of two square": $\displaystyle (x^2-y^2)(x^2+y^2)$. Now, you can factor $\displaystyle x^2-y^2$ again but since you have an even power now, you cannot factor [tex]x^2+y^2[tex] further.