Final answer:
To multiply the polynomials (5z - 5) and (25z^2 + 25z + 25), distribute each term of the first polynomial across the second polynomial, then combine like terms to get the final result: 125z^3 - 125.
Step-by-step explanation:
The student has asked to multiply the polynomials (5z - 5) by (25z2 + 25z + 25). To do this, apply the distributive property where each term of the first polynomial is multiplied by each term of the second polynomial. The steps are as follows:
- Multiply 5z by each term in the second polynomial: (5z × 25z2) + (5z × 25z) + (5z × 25)
- Multiply -5 by each term in the second polynomial: (-5 × 25z2) + (-5 × 25z) + (-5 × 25)
- Combine the results from steps 1 and 2.
Performing the multiplication gives us:
(125z3 + 125z2 + 125z) + (-125z2 - 125z - 125)
Combining like terms, we find the final result:
125z3 - 125