Step 3: An Algebraic Perspective
As most readers are hopefully aware, all numbers n the base 10 number system (and number systems of any other base, for that matter) consist of a number of digits. Each digit represents a multiple times a power of 10 (or whatever the number system's base is). So, for example, given a number like 52, we could rewrite it as 5*10+2.
Algebraically speaking, we can express any 3-digit number as:
ax+b (where a, and b are integers).
So, suppose we wanted to multiply 2 2-digit numbers. We can express them in polynomial form. Then, by foiling:
(ax+b)(cx+d) = acx2+(ad+bc)x+bd
Read on to see how we take the algebraic multiplication to higher numbers of digits.
Algebraically speaking, we can express any 3-digit number as:
ax+b (where a, and b are integers).
So, suppose we wanted to multiply 2 2-digit numbers. We can express them in polynomial form. Then, by foiling:
(ax+b)(cx+d) = acx2+(ad+bc)x+bd
Read on to see how we take the algebraic multiplication to higher numbers of digits.
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