Find the product. Simplify your answer. -2q²(-2q² + 2q)
Understand the Problem
The question is asking to find the product of a polynomial multiplied by a monomial and to simplify the answer.
Answer
The simplified product is $4q^4 - 4q^3$.
Answer for screen readers
The simplified product is $4q^4 - 4q^3$.
Steps to Solve
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Distribute the Monomial We need to distribute the monomial $-2q^2$ to each term in the polynomial $(-2q^2 + 2q)$. This means we will multiply $-2q^2$ by each term separately.
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Multiply the First Term Calculate the product of the first term: $$ -2q^2 \times -2q^2 = 4q^4 $$
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Multiply the Second Term Now, calculate the product of the second term: $$ -2q^2 \times 2q = -4q^3 $$
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Combine the Results Now combine both results into a single polynomial: $$ 4q^4 - 4q^3 $$
The simplified product is $4q^4 - 4q^3$.
More Information
This type of problem illustrates the process of multiplying a monomial by a polynomial, which is fundamental in algebra. Understanding this concept will help in solving more complex polynomial problems.
Tips
- Forgetting to change the sign when multiplying a negative by a negative, which can lead to incorrect positive results.
- Not applying the distribution correctly to each term in the polynomial.
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