Find the product. Simplify your answer: -x(-x² - 6)
Understand the Problem
The question is asking to find the product of the given expression, which involves multiplying and simplifying the polynomial. The expression to be simplified is -x(-x² - 6).
Answer
The simplified expression is $x^3 + 6x$.
Answer for screen readers
The simplified expression is $x^3 + 6x$.
Steps to Solve
- Distribute the negative x To simplify the expression, we will distribute the $-x$ across the polynomial $(-x^2 - 6)$.
[ -x \cdot (-x^2) + (-x) \cdot (-6) ]
- Calculate the products Now we'll do the multiplication for each term obtained during distribution.
[ -x \cdot (-x^2) = x^{3} ] [ -x \cdot (-6) = 6x ]
- Combine the terms Now we combine the results from the previous step.
The expression simplifies to:
[ x^3 + 6x ]
The simplified expression is $x^3 + 6x$.
More Information
This expression represents a polynomial that is a combination of a cubic term and a linear term. Such polynomials can be useful in various applications, from algebra to calculus.
Tips
- Forgetting to distribute the negative sign properly, which could lead to incorrect signs in the final expression.
- Neglecting to collect like terms if there are multiple terms created after distribution.
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