RYS #	Don’t do this	Do this	Why
1	(x + 5)2 = x2 + 25	= x2 + 10x + 25	(a + b)2 = a2 + 2ab + b2 exponents do not distribute over addition or subtraction
2	write       x - 3/2  when you mean	write (x - 3)/2  or	order of operations
3		(cannot be simplified)	same reason as #1: think of it as
4 (calculator)	enter e3x as e^3x	enter e^(3x)	e^3x means e3x (order of operations)
5*	3x = 12 3x/3 = 12/3 x = 4	do it in your head, just write:  x = 4	you can move the multiplier 3 to the other side of the equation by making it a divisor
6*	x + 1 =    5      -1     -1 ------------- x       =    4	do it in your head, just write:  x = 4	you can just move the term 1 to the other side of the equation and change its sign
7	| x + 7| + 3 = x + 10	(cannot be simplified)	usually can’t just discard abs. value signs as if they were meaningless
8	log (a + b) = log a + log b	(cannot be simplified)	log (ab) = log a + log b can’t have it both ways!
9*	(x + 2)(x + 3) = x2 + 2x + 3x + 6	just write answer: x2 + 4x + 6	for a product like this, the OI of FOIL can be combined in your head
10*	(x + 3)2 = (x+3)(x+3) = x 2 +6x+9	just write the answer: x2 + 6x + 9	use the formula: (a + b)2 = a2 + 2ab + b2 and do it in your head
11	(by cancelling the x's)	fraction cannot be simplified	can’t cancel common terms out of numerator and denominator; can cancel factors: (a b)/b = a/1 = a
12 (calculator)	enter  as      x - 3/2	enter (x - 3)/2	order of operations
13	equation: x2 = 9 solution:  x =  = 3	solution: x =   =  3
14	-12 = 1	-12 = -1	order of operations.  (-1) 2 = 1
15	subtract a + b from x as follows: x - (a + b)  =  x - a + b	=  x - a - b	distribute the "-" sign to all terms in (a + b)

* not wrong, just inefficient/immature form for students doing college-level algebra