How was this done? lim z --> z_0. (z^3 - z^3_0)/(z - z_0)...

[Vol]

lim z --> z_0. (z^3 - z^3_0)/(z - z_0)
lim z --> z_0. (z^2 + zz_0 + z^2-0)(z - z_0)/(z - z_0)

How did we get from line 1 to line 2? Is this some kind of weird factoring technique?

 

[Steven G]

lim z --> z_0. z^3 - z^3_0/z - z_0
lim z --> z_0. (z^2 + zz_0 + z^2-0)(z - z_0)/z - z_0

How did we get from line 1 to line 2? Is this some kind of weird factoring technique?

What does z^3_0/z mean?

 

[Vol]

Vol

Nevermind. I got it. It is factoring. I will go review binomial factoring.

 

[Deleted member 4993]

lim z --> z_0. (z^3 - z^3_0)/(z - z_0)
lim z --> z_0. (z^2 + zz_0 + z^2-0)(z - z_0)/(z - z_0)

How did we get from line 1 to line 2? Is this some kind of weird factoring technique?

Hint:

a³ - b³ = (a - b)(a² + ab + b²)

 

[JeffM]

Nevermind. I got it. It is factoring. I will go review binomial factoring.

What you need to review is difference of powers.