Find the product. Simplify your answer. -4r(-4r^2 - 4r + 4)
Understand the Problem
The question is asking to find and simplify the product of the expression provided, which involves multiplying a monomial with a polynomial.
Answer
The product simplifies to $$ 16r^3 + 16r^2 - 16r $$
Answer for screen readers
The final answer is $$ 16r^3 + 16r^2 - 16r $$
Steps to Solve
- Distribute the Monomial Multiply the monomial (-4r) by each term in the polynomial (-4r^2 - 4r + 4):
[ -4r \cdot (-4r^2) + -4r \cdot (-4r) + -4r \cdot 4 ]
- Perform the Multiplications Calculate each multiplication:
-
First term: [ -4r \cdot (-4r^2) = 16r^3 ]
-
Second term: [ -4r \cdot (-4r) = 16r^2 ]
-
Third term: [ -4r \cdot 4 = -16r ]
- Combine the Results Put together the results from the multiplications:
[ 16r^3 + 16r^2 - 16r ]
- Final Expression The simplified product of the expression is:
[ 16r^3 + 16r^2 - 16r ]
The final answer is $$ 16r^3 + 16r^2 - 16r $$
More Information
This expression represents the results from multiplying a monomial by a polynomial. The coefficients and variables show how the original expressions interact through distribution.
Tips
- Forgetting to distribute to all terms: Make sure to multiply the monomial by each term in the polynomial.
- Sign errors: Be cautious with signs when multiplying negative and positive numbers.
AI-generated content may contain errors. Please verify critical information
