Simplifying algebraic expressions is an important skill you'll learn in Year 10 Math. It makes tough problems easier to solve and gets you ready for more complicated topics. Let’s go over some simple ways to simplify these expressions.

1. Combine Like Terms

The first step in simplifying an expression is to find and combine like terms. Like terms are terms that have the same variable and power.

Example: Look at the expression $3x + 5x - 2 + 4$. Here, $3x$ and $5x$ are like terms. When we combine them, we get:

$$3x + 5x = 8x$$

Next, let’s combine the constant numbers:

$$-2 + 4 = 2$$

Putting it all together, we get:

$$3x + 5x - 2 + 4 = 8x + 2$$

2. Use the Distributive Property

Another useful tool is called the distributive property. It says that $a(b + c) = ab + ac$. This is helpful when you need to simplify expressions inside parentheses.

Example: Consider the expression $2(x + 3)$. Using the distributive property, we can rewrite it like this:

$$2(x) + 2(3) = 2x + 6$$

3. Factoring Out Common Factors

Sometimes, you can also simplify an expression by factoring. This means taking out common parts.

Example: Look at the expression $6x + 9$. You can see both parts can be divided by 3:

$$6x + 9 = 3(2x + 3)$$

Conclusion

Simplifying algebraic expressions is all about organizing and reducing terms to make them easier to manage. By combining like terms, using the distributive property, and factoring, you’ll get better at simplification in Year 10! Keep practicing these techniques, and you’ll find that algebra can become much simpler.