# Algebra - Expanding

"Expanding" means **removing the** ( ) ... but we have to do it the right way!

( ) are called "parentheses" or "brackets"

Whatever is inside the ( ) needs to be treated as a "package".

So when multiplying: multiply by everything inside the "package".

### Example: Expand 3 × (5+2)

Answer:

It is now expanded.

We can also complete the calculation:

3 × (5+2) = **3 × 5** + **3 × 2**

= 15 + 6

= 21

## In Algebra

In Algebra putting two things next to each other usually means to multiply.

So **3(a+b)** means to multiply **3** by **(a+b)**

Here is an example of expanding, using variables **a**, **b** and **c** instead of numbers:

And here is another example involving some numbers. Notice the "·" between the 3 and 6 to mean multiply, so **3·6 = 18**:

Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:

In that case **−3 · -5 = +15** (a positive answer), but here is an example where the second part is negative:

So the second term ended up negative because **2x · −a = −2ax**, (it is also neater to write "−2ax" rather than "−2xa").

That was also interesting because of x being squared (x^{2})

Lastly, we have an example with three terms inside:

The same rule applies: multiply by everything inside the ().

And here is a hint: when a multiplication is obvious (like **a · 2**) do it straight away, but when it needs more thought (like **a · −b**) leave it for the next line.

## Many Times Many

How do we do something like this?

(x + 2y)(3x − 4y)

Read Multiplying Polynomialsto find out!

## Conclusion

Multiply by everything inside the ()

Do it in two stages:

- Write down the multiplications
- Then do the multiplications