Question

simplify the following: (2y-1) cdot(4y¹⁰ 2y⁹ 4y⁸ 2y⁷). express your answer as a polynomial with the degrees of the terms in decreasing order.

Answer 1

To simplify the given expression, we distribute (2y-1) across the second polynomial and combine like terms, resulting in the final simplified polynomial 8y¹ⁱ + 4y¹⁰ - 2y⁹ - 2y⁸.

Step-by-step explanation:

The student asked to simplify the expression (2y-1)(4y¹⁰ + 2y⁹ + 4y⁸ + 2y⁷) and express the result as a polynomial with the degrees of the terms in decreasing order. To simplify this expression, we need to distribute (2y−1) across each term in the second set of parentheses. Here are the steps:

1. Multiply 2y with each term: 8y¹ⁱ + 4y¹⁰ + 8y⁹ + 4y⁸.
2. Multiply -1 with each term: -4y¹⁰ - 2y⁹ - 4y⁸ - 2y⁷.
3. Add together the corresponding terms with the same degrees.

After performing these steps, the final polynomial in descending order is 8y¹ⁱ + 4y¹⁰ - 2y⁹ - 2y⁸.