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
(a0+a1*x+a2*x^2)(b0+b1*x+b2*x^2)
Now, rearrange them in descending powers of x
(a2x^2+a1x+ao)(b2x^2+b1x+bo) Now follow this example
http://image.tutorvista.com/cms/images/38/trinomial-multiplication.JPG
Next, multiply the second term of the first trinomial with each term of the second trinomial. Finally, multiply the third term of the first trinomial with each term of the second trinomial. Hence, the product of (2x2 + 2x + 1) and (3x2 + 5x + 2) is 6x4 + 16 x3 + 17x2 + 9x + 2.
To expand the given polynomial and write it in standard form, we need to multiply each term from the first summation expression (∑ a_i x^i) with each term from the second summation expression (∑ b_j x^j).
Here's a step-by-step approach on how to expand the polynomial:
1. Start by multiplying the first term from the first summation (∑ a_i x^i) with each term from the second summation (∑ b_j x^j).
(a_0 x^0)(b_0 x^0) = a_0 b_0 x^(0+0) = a_0 b_0 x^0
2. Move on to the second term from the first summation and multiply it with each term from the second summation.
(a_1 x^1)(b_0 x^0) = a_1 b_0 x^(1+0) = a_1 b_0 x^1
(a_1 x^1)(b_1 x^1) = a_1 b_1 x^(1+1) = a_1 b_1 x^2
3. Repeat this process for each term in the first summation, multiplying it with each term in the second summation.
(a_2 x^2)(b_0 x^0) = a_2 b_0 x^(2+0) = a_2 b_0 x^2
(a_2 x^2)(b_1 x^1) = a_2 b_1 x^(2+1) = a_2 b_1 x^3
(a_2 x^2)(b_2 x^2) = a_2 b_2 x^(2+2) = a_2 b_2 x^4
4. Continue this process for all terms in the first summation, multiplying each term with each term in the second summation.
5. Once you have multiplied all the terms, combine like terms by adding the exponents of x and by multiplying the coefficients.
6. The result will be the expanded polynomial in standard form.
It is important to note that the given polynomial's expansion and standard form will depend on the specific values assigned to the coefficients (a_i and b_j) and the exponents (i and j).