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Hi again Kath;
HAPPY THANKSGIVING!
You are like me.  When I was in school, the Holidays were an opportunity to catch-up on homework.  I never learned how to baste a turkey.  Larry is doing all of the cooking today.  I cannot even make the frozen corn.
(5x + 3)(x-4)
First, I would like to correct your English.  These are not brackets.  Brackets are [ and ].  These are parentheses.  We have to resolve two parenthetical equations.
Let's FOIL...
FIRST...(5x)(x)=5x2
OUTER...(5x)(-4)=-20x
INNER...(3)(x)=3x
LAST...(3)(-4)=-12
You may already know that a negative number multiplied by a positive number results in a negative number.
Therefore...
5x2-20x+3x-12
5x2-17x-12
 
(2x-1)2
This is...
(2x-1)(2x-1)
Let's FOIL...
FIRST...(2x)(2x)=4x2
OUTER...(2x)(-1)=-2x
INNER...(-1)(2x)=-2x
LAST...(-1)(-1)=1
4x2-2x-2x+1
4x2-4x+1

Comments

Brackets are a catch-all term for (), [], {}, etc.  We use the adjective "square" when describing [] so that they are called square brackets. (Q.v. http://en.wikipedia.org/wiki/Bracket)  The use of the word bracket is especially common in British mathematics.
 
Moreover, you are not resolving parenthetical equations, but rather simplifying expressions.

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