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Expand the product (x - 2)^2 (x + 2)^3. What is the product of the nonzero coefficients of the resulting expression, including the constant term?

 May 8, 2022
 #1
avatar+9676 
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Whenever you have (x+a)n and the exponent is bigger than 2, you want to use binomial theorem to expand it.

Otherwise, you can use sum of square identity (a + b)^2 = a^2 + 2ab + b^2.

 

 

Afterwards, you just expand it out like this:

 

 

 

And then expand each clump. It is troublesome, but it will work out nicely.

 May 8, 2022
 #2
avatar+2668 
0

We can write this as: 

 

Recall the identity: 

 

This means we can rewrite the equation as: 

 

We know that 

 

Now, we have: 

 

Can you expand this?

 May 9, 2022
 #3
avatar+9676 
0

This method is nicer and is easier to do! 

MaxWong  May 9, 2022

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