When solving mathematical expressions, it is often necessary to expand parentheses. This process ensures that we follow the correct order and arrive at the correct answer.

What are parentheses?

Parentheses tell you which part of the calculation has priority. In mathematics, we often use them to make groups:

🔹 Sums: (a + b)
🔹 Products: (a × b)
🔹 Combinations: 3(x + 4) (This actually means: 3 × (x + 4))

Expanding Parentheses

1. The "Arcs" Method

Multiply the number outside the parentheses by every term inside the parentheses.

a(b + c) = a · b + a · c

2. Negative Parentheses ⚠️

Is there a minus sign in front of the parentheses? Then all signs inside the parentheses flip (plus becomes minus, minus becomes plus).

-(a + b) = -a - b

Multiple Parentheses

For a calculation like (x + 2)(x + 3), you can use the table method to avoid forgetting any terms:

×	x	+3
x	x²	+3x
+2	+2x	+6

Result: x² + 3x + 2x + 6
Combine the x's: x² + 5x + 6

💡 Tip for success

Mathematics is a "doing sport". Always try to write down the steps on paper. Haven't calculated in a while? Then start with the table method, it is the safest!

When solving mathematical expressions, it is often necessary to expand parentheses. This process ensures that we follow the correct order and arrive at the correct answer.

The Parrot Beak Method 🦜

When multiplying two groups in parentheses, such as (x + 2)(x + 3), we use the arcs method. If you draw the arcs, you will see the shape of a parrot's beak appear!

The arcs show exactly which combinations you need to make.

Here is how it works step by step:

Upper beak (left): x · x = x²
Upper beak (right): x · 3 = 3x
Lower beak (left): 2 · x = 2x
Lower beak (right): 2 · 3 = 6

All together: x² + 3x + 2x + 6 → x² + 5x + 6