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Question 7001: A multipling procedure for 28x32.
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! I don't exactly know what you mean. Are you looking for another way to solve 28 * 32 besides how you were taught in elementary?
I know a trick you can use with this kind of problem. Say we have two numbers m and n that we are to multiply. It's easiest if their one's digits add up to 10, and their tens digits have a difference of 1.
There is a topic in polynomials that is brought out to students' attention (usually refered to as the difference of squares) - What happens when you perform FOIL on a product of the form (a + b)(a - b)? It becomes a^2 - b^2. We'll use that trick to solve this type of multiplication problem.
We can say that 32 = 30 + 2 and 28 = 30 - 2. So we have the product (30 + 2)(30 - 2). That's EXACTLY in the form (a + b)(a - b). If (a + b)(a - b) really equals a^2 - b^2, then we can say 30^2 - 2^2 which is 900 - 4, which finally equals 396.
Another example: 44 * 56. 44 = 50 - 6, and 56 = 50 + 6. (50 + 6)(50 - 6) = 50^2 - 6^2 = 2500 - 36 = 2464.
So how would two numbers qualify for this type of multiplication again?
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