How to Expand and Simplify Binomials: Step-by-Step Guide
Quick Answer
To expand and simplify the expression (b + 8)(3b - 6), use the distributive property to multiply each term. The result is 3b² + 18b - 48.
When working with binomials like (b + 8)(3b - 6), it's essential to understand the distributive property or the FOIL method, which stands for First, Outside, Inside, and Last. This method helps you multiply two binomials systematically. Let's break it down step by step:
1. **First**: Multiply the first terms in each binomial. Here, it's b (from the first binomial) multiplied by 3b (from the second binomial). This gives us **3b²**.
2. **Outside**: Next, multiply the outer terms. This means b (from the first binomial) multiplied by -6 (from the second binomial), resulting in **-6b**.
3. **Inside**: Now, focus on the inner terms: 8 (from the first binomial) multiplied by 3b (from the second binomial). This gives us **24b**.
4. **Last**: Finally, multiply the last terms of each binomial: 8 (from the first binomial) and -6 (from the second binomial), resulting in **-48**.
Now, combine all these results together: 3b², -6b, 24b, and -48. The next step is to combine like terms. You have -6b and 24b, which combine to give you **18b**. Thus, your final simplified expression is:
**3b² + 18b - 48**.
This method can be applied in various real-world contexts, such as calculating areas or optimizing functions in algebra. Mastering this technique can significantly boost your confidence in handling polynomial expressions effectively. If you encounter more complex binomials or polynomials in your studies, remember that practicing the distributive property will always yield accurate results. Keep practicing, and you'll become proficient in expanding and simplifying expressions in no time!
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