Expanding brackets is a really important skill in algebra, especially for Year 10 students who are studying the British curriculum. It's the first step to simplifying expressions and solving equations. Let's go through the simple steps to expand brackets in algebraic expressions.

Step 1: Find the Brackets

First, look for the brackets in the expression you want to expand. Brackets usually signify multiplication. For example, in the expression $3(x + 2)$, the part $(x + 2)$ is in brackets.

Step 2: Use the Distributive Property

Next, we use the Distributive Property. This is a math rule that says $a(b + c) = ab + ac$. This means you multiply each term inside the brackets by the term outside.

Example 1:

For the expression $3(x + 2)$:

• First, multiply $3$ by $x$ to get $3x$.
• Then, multiply $3$ by $2$ to get $6$.
• Finally, combine the results to find: $3(x + 2) = 3x + 6$.

Step 3: Multiple Sets of Brackets

If you have more than one set of brackets, you’ll need to repeat these steps for each one. Don't forget to combine like terms!

Example 2:

Look at $2(a + 3) + 4(b + 1)$:

• First, expand $2(a + 3)$ to get $2a + 6$.
• Then expand $4(b + 1)$ to get $4b + 4$.
• Now, combine the results: $2a + 6 + 4b + 4 = 2a + 4b + 10$.

Step 4: Pay Attention to Signs

It’s super important to watch the signs (the plus and minus) in front of the terms in brackets. Negative signs can change the results a lot!

Example 3:

For $-2(x - 5)$:

• Here, the $-2$ has to be distributed to both terms inside the bracket.
• First, multiply $-2$ by $x$ to get $-2x$.
• Then, multiply $-2$ by $-5$ to get $10$ (because a negative times a negative is a positive).
• So, $-2(x - 5) = -2x + 10$.

Step 5: Practice, Practice, Practice!

The best way to get good at expanding brackets is to practice. Try out different expressions and set challenges for yourself with different levels of difficulty.

Practice Problems:

1. Expand $4(y + 2)$.
2. Expand $-3(m - 4) + 5(2 + m)$.
3. Expand $5(a + b)(c)$.

Wrap Up

Expanding brackets is a foundational skill in algebra that will help you with even harder topics as you learn more math. Remember the steps: find the brackets, use the Distributive Property, watch the signs, and keep practicing. Before you know it, you’ll be expanding brackets like a pro!