Perfect Square

• a positive integer which is the square of some other integer, i.e. can be written in the form n² for some integer n.
• Examples: 1, 4, 9, 16, 25, 36, 49, ... See square number.
• an algebraic expression that can be factored as the square of some other expression, e.g. a² ± 2ab + b² = (a ± b)². (see Square (algebra)).

Using differences of squares as multiplication

• $10\backslash times\; 10\; =\; 10^2\; -\; 0^2\; =\; 100\; -\; 0\; =\; 100$
• $9\backslash times\; 11\; =\; 10^2\; -\; 1^2\; =\; 100\; -\; 1\; =\; 99$
• $8\backslash times\; 12\; =\; 10^2\; -\; 2^2\; =\; 100\; -\; 4\; =\; 96$
• $7\backslash times\; 13\; =\; 10^2\; -\; 3^2\; =\; 100\; -\; 9\; =\; 91$

• $A\backslash times\; B\; =(A+B)/2^2\; -(A-B)/2^2$

• $A\backslash times\; B\; =\; A\backslash times\; (B-1)\; +\; A$

• $27\backslash times\; 34\; =33+\; 27\; =-\; 3^2+\; 27\; =\; 900\; -\; 9\; +\; 27\; =\; 918$

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