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?
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.
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?