Find the product. Simplify your answer: 3(-4p² - p - 2).
Understand the Problem
The question is asking to multiply a polynomial by a monomial (3 and the polynomial -4p² - p - 2) and then simplify the resulting expression.
Answer
The simplified product is $$-12p² - 3p - 6$$.
Answer for screen readers
The simplified product is: $$-12p² - 3p - 6$$
Steps to Solve
-
Distributing the Monomial To multiply the monomial $3$ by each term in the polynomial $-4p² - p - 2$, we will distribute $3$ across the terms.
-
Calculating Each Product First, we will calculate:
- $3 \cdot (-4p²)$
- $3 \cdot (-p)$
- $3 \cdot (-2)$
Calculating these gives us:
- $3 \cdot (-4p²) = -12p²$
- $3 \cdot (-p) = -3p$
- $3 \cdot (-2) = -6$
- Combining the Results Combine the results from the calculations: $$-12p² - 3p - 6$$
This is the simplified expression.
The simplified product is: $$-12p² - 3p - 6$$
More Information
When multiplying a polynomial by a monomial, each term of the polynomial is multiplied by the monomial separately. This process ensures that all terms are accounted for in the final expression.
Tips
- Forgetting to distribute the monomial to all terms in the polynomial. Ensure that each term is multiplied by the monomial.
- Incorrect sign calculation when multiplying negative numbers. Always double-check your signs.
AI-generated content may contain errors. Please verify critical information
