Question

exponents and polynomials
multiplying a univariate polynomial by a monomial with a negative...
rewrite without parentheses.
-3w⁶(3w³ + 6w - 7)
simplify your answer as much as possible.

Explanation:

Step1: Distribute the monomial

We use the distributive property \(a(b + c + d)=ab+ac + ad\) here. So, \(-3w^{6}\times3w^{3}+(-3w^{6})\times6w+(-3w^{6})\times(-7)\)

Step2: Multiply the coefficients and add exponents for variables

For the first term: \(-3\times3 = - 9\), and \(w^{6}\times w^{3}=w^{6 + 3}=w^{9}\), so the first term is \(-9w^{9}\)
For the second term: \(-3\times6=-18\), and \(w^{6}\times w = w^{6+1}=w^{7}\), so the second term is \(-18w^{7}\)
For the third term: \(-3\times(-7) = 21\), and \(w^{6}\) remains as it is, so the third term is \(21w^{6}\)

Answer:

\(-9w^{9}-18w^{7}+21w^{6}\)