The Distributive property is a * (b + c) = (a * b) + (a * c). What that means is that if you’re multiplying a number by an expression which is the sum of two terms or numbers, you can distribute the term (a) into the expression. Of course you can always evaluate (b + c) and then multiply it by a but sometimes distributing a into the expression will help you in algebra or even number calculation.
For example if you were multiplying 90 * 102, you could do the multiplication and get the answer. That would take some time. To save some time, you can use the distributive property as follows:
90 * 102 = 90 * (100 + 2) = (90 * 100) + (90 * 2) = 900 + 180 = 1080
There’s one more way that you can use the same property to simplify more complicated multiplications. Take the following example:
92 * 102 = (90 + 2) * (100 + 2)
This the same thing as (a + b) * (c + d) = ac + ad + bc + bc.
So you have to distribute both a and b into the second expression. And so the previous calculation becomes:
92 * 102 = (90 + 2) * (100 + 2) = (90 * 100) + (90 * 2) + (2 * 100) + (2 * 2) = 9000 + 180 + 200 + 4 = 9384
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