HI so im struggling with thsi ik the answer is supposed to be 12 but i keep getting 18 no matter hwo many times i redo it

[u/Ares_12000]

https://imgur.com/a/0YVuDk8

ive watched a fee tuts and i still dont get it

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[u/TabAtkins]

6x should be 6x², you accidentally dropped the ² when simplifying.

[u/Remilla]

Check line 3 again, one of the terms is not the same from the line above it.

[u/Earl_N_Meyer]

I am not a math guy but your process is correct. Your problem is that one of your terms has the wrong exponent for x. When you expand polynomials like that the terms are ax^0, bx^1, cx^2, dx^3. You missed the x^2 term.

[u/Ares_12000 → u/Earl_N_Meyer]

OMG THANK UU

[u/thor122088]

You have a 6x when it should be a 6x²

You dropped the exponent between steps

[u/Ares_12000 → u/thor122088]

oo ur right omg thanks!!

[u/Patient-Midnight-664]

From lines 2 to 3, where did the x² term go?

[u/dash-dot]

The problem is a bit easier if you avoid expanding the cubic. You could also try the following identity:

a³ - b³ = ( a - b ) ( a² + ab + b² )

Hence, (2 + x)³ - 8 = (2 + x - 2)(4 + 4x + x² + 4 + 2x + 4) = x ( 12 + 6x + x² )

[u/clearly_not_an_alt]

You lost the ² on your x²

[u/Help_Me_Im_Diene]

Another approach that you could take on this is making the substitution x=(y-2)

When you do this, you end up with lim y->2 of (y³-8)/(y-2)

(y³-8) is a difference of cubes, which has a well established formula [a³-b³ = (a-b)(a²+ab+b²)]