SOLUTION: m exponent 2 (m exponent 3 minus y exponent 3) we need to simplify each expression. so is it m exponent 6 - y exponent 3?

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Question 548440: m exponent 2 (m exponent 3 minus y exponent 3) we need to simplify each expression.
so is it m exponent 6 - y exponent 3?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
m%5E2%28m%5E3-y%5E3%29?
You could write that as m^2(m^3-y^3). (The caret symbol, "^" is used to show that what follows immediately after that is an exponent).
m%5E2%28m%5E3-y%5E3%29=m%5E2%2Am%5E3-m%5E2%2Ay%5E3=m%5E5-m%5E2y%5E3
The first equal sign
m%5E2%28m%5E3-y%5E3%29=m%5E2%2Am%5E3-m%5E2%2Ay%5E3
is applying the distributive property.
m%5E2 is multiplied times the entire parenthesis, not just times m%5E3.
Imagine buying three units of an item that costs $9.95. The price per unit is ($10-$0.05). The cost of three of those is
3($10-$0.05)= 3($10)-3($0.05)=$29.85
If the cashier calculated your cost as
3($10)-$0.05=$29.95
you would complain, wouldn't you?
The second equal sign
m%5E2%2Am%5E3-m%5E2%2Ay%5E3=m%5E5-m%5E2y%5E3
uses the fact that when multiplying powers of the same base you get a power (of the same base) with an exponent equal to the sum of the exponents in the factors.
m%5E2%2Am%5E3=%28m%2Am%2Am%29%2A%28m%2Am%29=m%2Am%2Am%2Am%2Am=m%5E5