Commonly Missed Algebra Facts 1 x 2 a 2 x a x 2 a 2 x a Put in nonzero numbers for x and a and you will see this fact Graph Y 1 x 2 2 a Y2 x a for any nonzero a They are not the same 2 2 You should always remember the graph of y a x is a semicircle but y a x is a line In general exponents do not distribute over sums and differences For another example 3 3 x 8 x 2 That is x 3 8 1 3 x 2 2 Always use parentheses when multiplying by a sum or difference a x 1 ax a If you lazily write a x 1 this is not an equal expression Students sometimes misread their own work Do this even if a is a minus sign in which case a 1 Write 5 x 1 5 x 1 3 Dividing by sums This really belongs in part 1 1 x a 1 x 1 a That is x a 1 x 1 a 1 Try it with nonzero numbers 4 Cancellation in division You can t cancel until you factor it out of the numerator and the denominator You cannot cancel the x in either of the expressions However you can cancel x from x 2 x 2 2x 4x x x 2 x x 4 x 2 x 4 x 2 x 4 x x 2 if x 0
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