Final answer:
The task is to multiply the monomial 6a²x by each term in the polynomial (9a² - 4bcx² + 6abx), applying the distributive property. The final result is 54a⁴x - 24a²bcx³ + 36a³bx².
Step-by-step explanation:
The student has asked to perform the indicated operation of multiplying a polynomial by a monomial. Specifically, the operation is to multiply 6a²x by the polynomial (9a² - 4bcx² + 6abx). To solve this, we apply the distributive property, where the monomial is multiplied by each term in the polynomial separately.
Here is the step-by-step solution:
- Multiply 6a²x by 9a² to get 54a⁴x.
- Multiply 6a²x by -4bcx² to get -24a²bcx³.
- Multiply 6a²x by 6abx to get 36a³bx².
Combining these results gives us the final answer:
54a⁴x - 24a²bcx³ + 36a³bx².