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:

brackets #1

further examples:

brackets #2

 

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: brackets #3

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

brackets #4

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

brackets #5

Add the two results together.

brackets #6

 

back to top

 

Example #1

brackets #7

Example #2

brackets #8

Example #3

brackets #9

 

back to top

 

Squared Brackets

brackets #10

note: a common mistake

brackets #11

 

back to top

 

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:

brackets #12

 

back to top

 

Factorising Quadratic Expressions

This is best illustrated with an example:

brackets #13

 

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


so

brackets #14


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


these are the choices: (+3)(+4), (-3)(+4), (+3)(-4) or (-3)(-4)


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


therefore

brackets #15

 

back to top

 

Example #1

brackets #16

 

Example #2

brackets #17

 

Example #3

brackets #18

 

 

back to top

 

Contact GCSE Maths Tutor here - info@gcsemathstutor.com

 

Google

A FREE resource

    mechanics

    matter

    nuclear phys.

    quantum mechs.

    electricity

    thermal phys.

    waves

    optics

    fields