Home >> Algebra - Brackets

**Coursework Notes - Algebra**

**Brackets**

[single term outside ][ two pairs brackets ][ difference of two squares ]

[ multiplying out - square brackets ][ factorising - simple ][ factorising quadratics ]

__Multiplying Out(expanding) - a pair of brackets with a single term infront__

The term outside the brackets multiplies each of the terms in turn inside the brackets.

example:

further examples:

__Multiplying Out(expanding) - two pairs of brackets__

Think of the two terms in the first bracket as separate single terms infront of a pair of brackets.

example:

Multiply the **contents** of the 2nd bracket by the **1st term** in the 1st bracket.

Multiply the **contents** of the 2nd bracket by the **2nd term** in the 1st bracket.

Add the two results together.

__Example #1__

__Example #2__

__Example #3__

__Squared Brackets __

** note**: a common mistake

__Difference of Two Squares __

__Brackets - Simple Factorising__ - This involves taking out a common term from each expression and placing it infront of the brackets.

examples:

__Factorising Quadratic Expressions __

This is best illustrated with an example:

You must first ask yourself which two factors when multiplied will give **12** ?

The factors of 12 are : ........**1 x 12**, ..............**2 x 6**, ...............**3 x 4**

Now which numbers in a group added or subtracted will give **7** ?

**1 x 12** gives 13, 11 ..............**2 x 6** gives 8, 4 .....................**3 x 4** gives 7, 1

so

which of the '+' & '-' terms makes **+12**? ........and when added gives **-7**?

clearly, **(-3)(-4)** are the two factors we want

therefore

__Example #1__

__Example #2__

__Example #3__

[ About ] [ FAQ ] [ Links ] [ Terms & Conditions ] [ Privacy ] [ Site Map ] [ Contact ]