NOTE: before you answer this question, please be aware that there aren't meant to be any full stops after the '2' or the 'i=0'. Also the underscores '-' represent how the following number is meant to be a lower case number. The ^ represents root numbers. PLEASE HELP ME

Expand the following polynomial and write it in standard form:

2. 2
(∑ a_i x^i )(∑ b_j x^j )
i=0. j=0

To expand the given polynomial (∑ a_i x^i )(∑ b_j x^j ) and write it in standard form, you need to multiply each term from the first summation (∑ a_i x^i) by each term from the second summation (∑ b_j x^j) and then combine like terms.

Let's break down the steps to expand and simplify the polynomial:

Step 1: Write out the two summations:
(∑ a_i x^i )(∑ b_j x^j )

Step 2: Start multiplying each term from the first summation (∑ a_i x^i ) with every term from the second summation (∑ b_j x^j ). This will give us a set of terms with various powers of x.

For example, if we have the terms a_0 x^0 and b_1 x^1, we would multiply them as follows:

(a_0 x^0)(b_1 x^1) = a_0 b_1 x^(0+1) = a_0 b_1 x^1

Continue doing this for all possible combinations of terms from (∑ a_i x^i ) and (∑ b_j x^j ).

Step 3: Combine like terms. This means adding together terms that have the same power of x.

For example, if you have terms like 3x^2 and 5x^2, you would combine them as follows:

3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2

Do this for all the terms you obtained in Step 2.

Step 4: Write the expanded polynomial in standard form by arranging the terms in descending order of powers of x.

For example, the standard form of the expanded polynomial would look something like:

c_n x^n + c_(n-1) x^(n-1) + ... + c_2 x^2 + c_1 x + c_0

Where c_i represents the coefficients of each term.

Remember to simplify the polynomial as much as possible by combining like terms and rearranging the terms in standard form.

Please provide the specific coefficients (a_i and b_j) in (∑ a_i x^i ) and (∑ b_j x^j ) so I can help you with the step-by-step expansion and simplification of the polynomial.