Sarabande
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#1
Report Thread starter 7 years ago
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I had to differentiate x^3(2x+6)^4

I got down to 8x^3(2x+6)^3 + 3x^2(2x+6)^4

According to the solution bank this is correct but you have to simplify it down afterwards to 2x^2(2x+6)^3(7x+9)

Anyone can explain how that works please?
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Sir Cumference
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Your expression contains two terms and both (2x+6)^3 and x^2 are factors of both of them. That means we can take (2x+6)^3 and x^2 outside the expression:

\displaystyle x^2(2x+6)^3 \left[8x+3(2x+6)\right]

Does this make sense and can you finish the simplification?
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Sarabande
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(Original post by notnek)
Your expression contains two terms and both (2x+6)^3 and x^2 are factors of both of them. That means we can take (2x+6)^3 and x^2 outside the expression:

\displaystyle x^2(2x+6)^3 \left[8x+3(2x+6)\right]

Does this make sense and can you finish the simplification?
Why does the 8x go into the bracket with the higher power?
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Sir Cumference
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(Original post by Sarabande)
Why does the 8x go into the bracket with the higher power?
I don't really understand your question. Could you try to explain again?

Try expanding the expression that I posted and you should see that it is equal to the two terms in your derivative.
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Sarabande
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#5
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I gave it a little thought. It makes perfect sense now. Thanks.
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