Questions: Exponents and Polynomials Multiplying a univariate polynomial by a monomial with a negative. Rewrite without parentheses. -4 w^4(-5 w^2+2 w+9) Simplify your answer as much as possible.

Solution Steps

To simplify the expression \(-4 w^{4}(-5 w^{2}+2 w+9)\), we need to distribute the monomial \(-4 w^{4}\) across each term inside the parentheses. This involves multiplying \(-4 w^{4}\) by each term \(-5 w^{2}\), \(2 w\), and \(9\) separately. After performing these multiplications, we combine the results to get the simplified polynomial.

We start with the expression: \[ -4 w^{4}(-5 w^{2} + 2 w + 9) \] We will distribute \(-4 w^{4}\) to each term inside the parentheses.

Calculating each term:

1. \(-4 w^{4} \cdot -5 w^{2} = 20 w^{6}\)
2. \(-4 w^{4} \cdot 2 w = -8 w^{5}\)
3. \(-4 w^{4} \cdot 9 = -36 w^{4}\)

Now, we combine the results from the multiplications: \[ 20 w^{6} - 8 w^{5} - 36 w^{4} \]

Final Answer