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