Welcome to our lesson on one of the fundamental skills in algebra: combining like terms. When working with algebraic expressions, it’s crucial to simplify them by combining terms that are alike. Today, we’ll learn exactly how to do that.
First, what does it mean to combine like terms? Like terms are terms that have the same variable raised to the same power.
For example, 2x and 5x are like terms because they both have the variable ‘x’ to the power of 1.
However, 2x and 2x² are not like terms because the powers are different.
To combine like terms, simply add or subtract their coefficients. A coefficient is a number in front of the variable.
Let’s say we have the expression 3x + 2x.
Since these terms are alike,
we add the coefficients 3 and 2 to get 5x.
So, 3x + 2x simplifies to 5x.
Now, let’s see how this works with a real-life example. Imagine you’re organizing your bookshelf.
You have 4 science books, 7 math books, and then you get 3 more science books.
How many science books do you have now?
Combine the like terms, 4 science books plus 3 science books, which equals 7 science books.
But what if there’s subtraction involved?
Suppose you have 10x – 3x. Just like addition, you subtract the coefficients because the terms are like. So, 10x – 3x equals 7x.
Sometimes, expressions are a bit more complex, like 5x + 3 – 2x + 4. To combine like terms, first find the like terms. Here, 5x and -2x are like terms, and so are 3 and 4. Combining them, we get 3x + 7.
In summary, combining like terms is about simplifying expressions to make them easier to work with. Always look for terms with the same variable and power, add or subtract the coefficients, and you’re on your way to mastering algebraic expressions. It’s a skill that will serve you well in algebra and beyond. So practice it, and you’ll see just how handy it can be.
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