How to Correctly Multiply Binomials: A Student's Guide
Quick Answer
To multiply binomials, use the distributive property by multiplying each term in the first binomial by each term in the second. For example, when multiplying (2x - 5)(x + 12), you get 2x² + 24x - 5x - 60.
Multiplying binomials is a fundamental skill in algebra that can help you solve a variety of mathematical problems. The process involves using the distributive property, which states that you multiply each term in one polynomial by each term in the other. Let's break down the multiplication of the binomials (2x - 5)(x + 12) step by step.
First, we identify the terms in each binomial. In (2x - 5), the terms are 2x and -5. In (x + 12), the terms are x and 12. To find the product, we perform the following multiplications:
1. Multiply the first term of the first binomial by each term of the second binomial:
- 2x * x = 2x²
- 2x * 12 = 24x
This gives us the first two terms of our result: 2x² + 24x.
2. Next, multiply the second term of the first binomial by each term of the second binomial:
- -5 * x = -5x
- -5 * 12 = -60
This adds the next two terms to our result: -5x - 60.
Now, we combine all the terms we've calculated:
2x² + 24x - 5x - 60.
Next, we can combine like terms. In this case, the like terms are 24x and -5x:
2x² + (24x - 5x) - 60 = 2x² + 19x - 60.
So, the final expression when multiplying (2x - 5)(x + 12) is 2x² + 19x - 60.
It's essential to be careful with each multiplication step, as small mistakes can lead to incorrect answers. For instance, if a student mistakenly wrote 2x instead of 2x² when multiplying 2x by x, it would throw off the entire calculation. This is why double-checking your work is crucial.
In real-world applications, understanding how to multiply binomials can help in areas such as physics, engineering, and economics, where you often deal with equations that model various phenomena. Mastering these concepts not only prepares you for more advanced topics in math but also enhances your problem-solving skills.
For further practice, try multiplying other sets of binomials using the same method—distributing each term systematically. As you practice, you will become more comfortable with recognizing and correcting any mistakes in your calculations.
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