Is my answer book wrong?

[Malfix25]

So, my math homebook has the following exercise: 2^{n - 3}b^{2n - 2}(b² - 2^{5 - n}b)

When I work out the problem, this is the answer I get: 2^{n - 3}b^{2n - 1} - 4²b^{2n - 1} (Which is equal to 2^{n - 3}b^{2n - 1} - 16b^{2n - 1})

But, the solution key to my book shows that this is the answer:

2^{n - 3}b^{2n - 1} - 4b^{2n - 1}

So, did my answer book make a mistake, or am I the one doing so?

 

[Deleted member 4993]

So, my math homebook has the following exercise: 2^{n - 3}b^{2n - 2}(b² - 2^{5 - n}b)
When I work out the problem, this is the answer I get: 2^{n - 3}b^{2n - 1} - 4²b^{2n - 1} (Which is equal to 2^{n - 3}b^{2n - 1} - 16b^{2n - 1})
But, the solution key to my book shows that this is the answer:
2^{n - 3}b^{2n - 1} - 4b^{2n - 1}
So, did my answer book make a mistake, or am I the one doing so?

2^n-3 * 2^5-n =2^n-3+5-n = 2²

The answer book is correct

 

[Malfix25]

Oh duh! My mistake lay where I multiplied the 2^n-3 * 2^5-n, I multiplied the coefficients as well, and got 4², instead of 2² Man it's been too long! Never would have thought I would have forgotten something so fundamental. I guess the saying "use it or lose it" is true!? Thanks man!