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SIMPLIFYING (a + b)2 and (a - b)2
Jump right to the exercises!
Here are two very important and common expressions:
(a + b)2 = (a + b)(a + b)
= a2 + ab + ab + b2
= a2 + 2ab + b2
(a - b)2 = (a - b)(a - b)
= a2 - ab - ab + b2
= a2 - 2ab + b2
You should (eventually) be able to multiply out expressions like these without writing
down any intermediate results.
Be careful! One of the most common algebra mistakes is to think that
(a + b)2 is equal to a2 + b2 .
NOT SO!!!
You've got the Firsts ("F") and the Lasts ("L") but have left out the Outers ("O") and
the Inners ("I")!
One of my students (Ian Sullivan) came up with a memory device for this situation:
Okay, square—go foil yourself!
EXAMPLES
Remember to use the "^" key for exponents.
(x - 2)2 = x^2 - 4x + 4
You MUST type the terms in the order indicated here for your answer to be recognized as correct.
That is, even though 4 - 4x + x^2 is a correct answer, it isn't recognized as correct
by this program.
(3x + y)2 = 9x^2 + 6xy + y^2
Variables MUST be typed in the order they appear, going from left to right, for your answer to be recognized
as correct.
That is, even though 9x^2 + 6yx + y^2 is a correct answer, it isn't recognized as correct
by this program.