# Thread: bracket expansion and differentiation

1. ## bracket expansion and differentiation

need to multiply

(x^2-1)^4

I get

-20x^9+32x^7-12x^5

Then i need to differentiate this 4 times

d^4/dx^4 (-20x^9+32x^7-12x^5)

I get

-10080x^6+6720x^4-720x^2

Is this right?

2. Originally Posted by ubhik
need to multiply

(x^2-1)^4

I get

-20x^9+32x^7-12x^5

Then i need to differentiate this 4 times

d^4/dx^4 (-20x^9+32x^7-12x^5)

I get

-10080x^6+6720x^4-720x^2

Is this right?
Think about this. Your highest power in the expansion will be $(x^2)^4 = x^8$. So you can't be right.

By the binomial theorem:
$(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$

You have $a = x^2$ and $b = -1$:

Thus
$(x^2 - 1)^4 = x^8 - 4x^6 + 6x^4 - 4x^2 + 1$

(I'd recommend making sure you know how to do it the long way as well. It's good practice.)

And make sure you take 4 derivatives. You only took 3.

-Dan

3. ok so for the differentiation of
[(x^2 - 1)^4]

i got

1680x^4 - 1440x^2 + 144

Is this right now?

4. Hello, ubhik!

I got: . $1680x^4 - 1440x^2 + 144$

Is this right now? . . . . Yes!
Good for you!

5. Originally Posted by ubhik
ok so for the differentiation of
[(x^2 - 1)^4]

i got

1680x^4 - 1440x^2 + 144

Is this right now?
[(x^2 - 1)^4] is an octic, so its derivative is a septic, so whatever anyone else says its derivative cannot be a quartic.

RonL

6. Originally Posted by ubhik
ok so for the differentiation of
[(x^2 - 1)^4]

i got

1680x^4 - 1440x^2 + 144

Is this right now?
$\frac{d}{dx} (x^2-1)^4 = 4 (x^2-1)^3 (2x)$

RonL

7. Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...

8. Originally Posted by ubhik
Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...
did the instructions tell you to expand the brackets first? i'd use the chain rule (as CaptainBlack did) 4 times and forget about binomial expansion.