multiplication of polynomials by polynomials.
2^n-3 b^2n-2 (b^2-2^5-n b)
I get 2^n-3 b^2n - 4^2 b^2n-1 but that is not right. I am stuck on the -4^2 part only. The rest is right.
To multiply polynomials, we need to distribute each term of the first polynomial to every term of the second polynomial. Let's go through the steps to find the correct multiplication of the given polynomials.
The given expression is:
2^n-3 b^2n-2 (b^2 - 2^5 - n b)
To simplify, we will start by multiplying each term of the first polynomial (2^n-3 b^2n-2) by each term of the second polynomial (b^2 - 2^5 - n b).
Step 1: Multiply the first term of the first polynomial (2^n) by each term of the second polynomial:
(2^n) * (b^2) = 2^n * b^2
(2^n) * (-2^5) = 2^n * (-2^5)
(2^n) * (n b) = 2^n * n b
Step 2: Multiply the second term of the first polynomial (-3 b^2n-2) by each term of the second polynomial:
(-3 b^2n-2) * (b^2) = - 3 b^2n-2 * b^2
(-3 b^2n-2) * (-2^5) = -3 b^2n-2 * (-2^5)
(-3 b^2n-2) * (n b) = -3 b^2n-2 * n b
Step 3: Combine the simplified terms obtained from Step 1 and Step 2 to get the final result:
2^n * b^2 + 2^n * (-2^5) + 2^n * n b + (-3 b^2n-2) * b^2 + (-3 b^2n-2) * (-2^5) + (-3 b^2n-2) * n b
Now, let's simplify these terms:
2^n * b^2 can be written as b^2 * 2^n
2^n * (-2^5) can be written as -2^5 * 2^n
2^n * n b can be written as n b * 2^n
(-3 b^2n-2) * b^2 can be written as b^2 * (-3 b^2n-2)
(-3 b^2n-2) * (-2^5) can be written as -2^5 * (-3 b^2n-2)
(-3 b^2n-2) * n b can be written as n b * (-3 b^2n-2)
So, the final result is:
b^2 * 2^n - 2^5 * 2^n + n b * 2^n + b^2 * (-3 b^2n-2) - 2^5 * (-3 b^2n-2) + n b * (-3 b^2n-2)
Now, you can simplify each term individually and combine like terms to get the final answer.