Combining like terms is an important idea in algebra that 10th-grade students need to understand well. Let's break it down:
What Are Like Terms?
- Like terms are parts of an expression that have the same variable and power.
- For example, in the expression 3x² + 5x², both 3x² and 5x² are like terms because they both use the variable x and the power 2.
- On the other hand, terms like 4xy and 5x² are not like terms. They cannot be combined because they differ in either the variable or the power.
Why Combining Like Terms Matters
- Combining like terms is super important for making algebraic expressions simpler. This makes it easier to solve equations.
- According to the school curriculum, students should learn to simplify expressions by combining like terms. This helps them get better at algebra and prepares them for more challenging topics later.
How to Combine Like Terms: Steps
- Find Like Terms: Look for terms in an expression that have the same variable and power.
- Add or Subtract Numbers: After finding like terms, combine them by adding or subtracting their numbers (called coefficients).
- For example, in 2a + 3a, you add the 2 and the 3 to get 5a.
- Rewrite the Expression: Replace the original like terms with the combined number.
- For example, 4x + 2x - 3 simplifies to 6x - 3.
Example of Combining Terms
Let’s look at the expression 3x + 4y + 5x - 2y:
- First, find the like terms: 3x and 5x are like terms, and 4y and -2y are also like terms.
- Now combine them:
- For x: 3x + 5x = 8x
- For y: 4y - 2y = 2y
- So, the simplified expression is 8x + 2y.
Success and Benefits
- Learning to combine like terms helps students do better on tests. Studies show that students who are good at this can score about 15% higher on the algebra parts of their exams compared to those who find it hard.
- Overall, mastering this skill sets the base for future math topics like simplifying expressions, solving equations, and understanding functions.