ok i get the whole FOIL thing but what if there's negative numbers? and what do you if there's an addition and a subtraction? ex. (mn-m^2)(-n+m)
you treat negative numbers just like positive numbers (for instance; (6x+3)(2x-2), 1st-6x*2x=12x^2, outer- 6x*-2=-12x, inner- 3*2x=6x, last- 3*-2=-6) get it?
Yes, you are correct. When using the FOIL method, negative numbers are treated the same way as positive numbers.
Now, let's apply the FOIL method to the expression you mentioned: (mn - m^2)(-n + m).
First, let's break down the FOIL acronym:
F stands for "First." This means we multiply the first terms of each binomial: (mn) * (-n) = -mn^2.
O stands for "Outer." This means we multiply the outer terms of each binomial: (mn) * m = mn^2.
I stands for "Inner." This means we multiply the inner terms of each binomial: (-m^2) * (-n) = mn^2.
L stands for "Last." This means we multiply the last terms of each binomial: (-m^2) * m = -m^3.
Now, we can combine these results:
-mn^2 + mn^2 + mn^2 - m^3.
The negative mn^2 and the positive mn^2 cancel each other out, so we are left with:
mn^2 - m^3.
So, the expression (mn - m^2)(-n + m) simplifies to mn^2 - m^3.
To summarize, when using FOIL, you treat negative numbers just like positive numbers. You multiply and combine them accordingly.