Suppose you have 5(6+3). You can find the result by doing 6+3=9 first and then multiply 5 by 9 = 45. However, you can also expand the brackets, by doing 5---6 + 5---3 = 30+15 = 45. Expanding brackets is especially useful when you have to deal with a variable. For example, 4(x+7) becomes 4x+28, while when expanded, x(x+5y) becomes 2x+5xy.
When all numbers inside and outside of the brackets have the same sign (they are all positive or negative), then the result you get is always positive. For example, on 6(5+4), all number are positive, therefore the result (6---5 + 6---4 = 30+24 = 54) is positive. Likewise, when you have -3[-7+(-9)], the result becomes (-3)---(-7)+(-3)---(-9)=21+27 = 48, which is again positive, as you multiplied same-sign numbers again (albeit negative by negative).
When you multiply positive by negative numbers the result is always negative. This means that when you expand brackets and one number is negative, the result is not an addition between the multiplication products but a subtraction. For instance, when you have 3(6-4) the result becomes 3---6 + 3---(-4) = 18-12. Even with a variable, such as x(x-4), the result is still a subtraction: (x---x) + x---(-4)=2x-4x.
Not all expanding brackets are as easy as doing two multiplications, as you may as well have two brackets to expand (called expanding double brackets). However, the procedure to expand the brackets remains largely the same. An example of expanding double brackets is: (x + 4)(x + 2), which becomes (x---x)+(2x)+(4x)+(4---2) = 2x+2x+4x+8 = 2x + 6x + 8.