Question

exponents and polynomials
multiplying a univariate polynomial by a monomial with a negative...
rewrite without parentheses.
$-9w^5\left(-9w^2 - 6w + 5\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Distribute the monomial

Multiply \(-9w^5\) with each term inside the parentheses:
\(-9w^5 \times (-9w^2) + (-9w^5) \times (-6w) + (-9w^5) \times 5\)

Step2: Multiply coefficients and add exponents

For the first term: \((-9) \times (-9) = 81\), \(w^5 \times w^2 = w^{5 + 2} = w^7\), so \(81w^7\)
For the second term: \((-9) \times (-6) = 54\), \(w^5 \times w = w^{5 + 1} = w^6\), so \(54w^6\)
For the third term: \(-9 \times 5 = -45\), so \(-45w^5\)

Step3: Combine the terms

Putting it all together: \(81w^7 + 54w^6 - 45w^5\)

Answer:

\(81w^7 + 54w^6 - 45w^5\)