-(-1%2F2x%5E3).jpeg "(-5x^5+2x^4-1/3x^3) (-1/2x^3)")
Multiplying Polynomials: A Step-by-Step Guide
This article will guide you through the process of multiplying the polynomials $(-5x^5+2x^4-\frac{1}{3}x^3)$ and $(-\frac{1}{2}x^3)$.
Understanding the Process
Multiplying polynomials involves distributing each term of one polynomial to every term of the other polynomial. This process is similar to the distributive property of multiplication in basic arithmetic.
Step-by-Step Solution
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Distribute the first term of the second polynomial:
- Multiply $-\frac{1}{2}x^3$ by $-5x^5$:
- $(-\frac{1}{2}x^3) * (-5x^5) = \frac{5}{2}x^8$
- Multiply $-\frac{1}{2}x^3$ by $2x^4$:
- $(-\frac{1}{2}x^3) * (2x^4) = -x^7$
- Multiply $-\frac{1}{2}x^3$ by $-\frac{1}{3}x^3$:
- $(-\frac{1}{2}x^3) * (-\frac{1}{3}x^3) = \frac{1}{6}x^6$
- Multiply $-\frac{1}{2}x^3$ by $-5x^5$:
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Combine the results:
- The final product of the multiplication is the sum of the results from step 1:
- $\frac{5}{2}x^8 - x^7 + \frac{1}{6}x^6$
- The final product of the multiplication is the sum of the results from step 1:
Simplified Solution
Therefore, the product of $(-5x^5+2x^4-\frac{1}{3}x^3)$ and $(-\frac{1}{2}x^3)$ is $\boxed{\frac{5}{2}x^8 - x^7 + \frac{1}{6}x^6}$.
Key Points to Remember
- Remember the rules of exponents: When multiplying variables with exponents, add the exponents together.
- Pay attention to signs: Be careful with negative signs when multiplying.
- Simplify the expression: Combine like terms after multiplying.
By following these steps, you can confidently multiply any two polynomials.