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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:

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

 

 

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Example #1

 

brackets #7

 

 

Example #2

 

brackets #8

 

 

Example #3

 

brackets #9

 

 

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Squared Brackets

 

brackets #10

 

note: a common mistake

 

brackets #11

 

 

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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

 

 

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


so

 

brackets #14

 


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



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


therefore

 

brackets #15

 

 

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Example #1

 

brackets #16

 

 

Example #2

 

brackets #17

 

 

Example #3

 

brackets #18

 

 

 

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