



We look
at "X times X + 4"



like any
other multiplication. 











Just do X
times X then X times 4 


and put
the answers together. 





We could
even multiply (X + 4) times (X + 4) 


Just
multiply X + 4 times 4 


and then
multiply X + 4 times X. 


Then put
the terms together in one place ... 











While it
may be easy to see what's going on 


writing
the multiplication like this, 


that's
not the way it's usually written. 


It's
usually written all on one line. 





We start
like this ... 


(X
+ 4)(X + 4)






Take the
first term in the first brackets 


and
multiply it by every term in the second bracket. 











Then take
the second term in the first bracket 


and
multiply it by every term in the second bracket. 











Now we
combine terms where we can. 


An X
^{2}
is not the same thing as an X. 


We can't
combine them. 


We can
combine the two different 4X terms we have. 





(X + 4)(X +
4) = X^{2} + 4X
+ 4X + 16 = X^{2}
+ 8X + 16 





The other
way we did these problems was easier to follow, 


but this
way uses a lot less paper to write. 


Math
types love to save space, 


so this
is the way it is usually done. 





More
Examples: 





(X
 5)(3X + 2) = 3X^{2} + 2X  15X 
10 = 3X^{2}  13X  10 





(5X
 3)(X  2) = 5X^{2}  10X  3X +
6 = 5X^{2}  13X + 6 





(X
+ 5)(2X + 4) = 2X^{2}  4X + 10X +
20 = 2X^{2} + 6X + 20 





copyright 2005 Bruce Kirkpatrick 
