## Removing Group Symbols

Sometimes, algebraic expressions are written in group symbols such as:

...in which you are asked to **expand** and **simplify **as seen below:

In these cases, the **distributive law** is used to remove group symbols:

### Examples:

## Binomial Products

A **binomial** expression consists of **two elements**, for example .

A set of two binomial expressions multiplied together is called a **binomial product**.

Binomial products are multiplied in **FOIL** order, that is:

**First**elements of both expressions.**Outer**elements of both expressions.**Inner**elements of both expressions.**Last**elements of both expressions.

Hence, the products are multiplied as follows:

### Examples:

Sometimes we see a **trinomial** that consists of three elements, and when multiplied it works the same way.

For example:

## Perfect Squares

Several characteristics of binomial products are shown below:

This is because:

The same can be done when:

...and the proof as follows:

(Remember: two negatives multiplied will yield a positive result)

There is also a the **difference of 2 squares** as seen below:

*Reflection: *What is the difference between and ?

### Examples:

Expand and simplify the following:

## Factorising

When factorising a binomial product, take out the highest common numbers (or pronumerals) that perfectly divide both elements without leaving a remainder. This also applies to trinomials, which will be discussed further in another section.

To factorise an expression, we use the distributive law.

*(Reflection:* Do you remember what HCF - **H**ighest **C**ommon **F**actor - means?)

### Examples:

Factorise:

1.

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The highest common factor is 3.

2.

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The common factor is .

3.

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If there are several common factors, take out all the factors. In this case, the common factor is .

Sometimes you will see expressions that are grouped in pairs, and therefore they could be factorised in pairs:

4.

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5.

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A special case of binomial products is:

6. Factorise

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7. Factorise

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There is also an interesting way to factorise the **sums and differences of 2 cubes**.

8. Factorise