The distributive property of multiplication over addition is simply this:  it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results.

That is,

    adding up the term first; then multiplying by the factor   =  multiplying each term by the factor first, then adding up the resulting terms

That is:       Factor(Term1 + Term2 + ... + TermN)  =   Factor(Term1) + Factor(Term2) + ..... + Factor(TermN)

If we call the Factor "a,"  and we call the terms "b", "c,"......"t", then this statement begins to look like a mathematical statement:

                                                  a(b + c + ....... + t)    = a(b) + a(c) + .... +a(t)

   EXAMPLE:    (The factor is 3, and the three terms  are 2, 7, -5)

                                                             3(2 + 7 - 5)  =   3(2) + 3(7) + (3)(-5)

                                                                 3(4)         =     6    +  21    -  15

                                                                   12         =   12

This is kinda cool, but you might wonder  what possible use it might be.  I mean, really, why wouldn't you ALWAYS add the terms together first, and avoid all that yukky multiplication?   Well, the answer is:   It comes in very useful when you have terms that cannot be added together first, because they are not like terms.

Case in point:    3(2x + 4).    We can't combine the 2x and the 4, because the first is x's and the second is 1's (four of them).  But, suppose this expression showed up in an equation like:

                             3(2x + 4) = 5

and we were asked to solve for x?  What to do?  We have to get the x's untied from the 1's, right?  Using the distributive property of multiplication over addition is what is going to let us solve this equation:

                           3(2x) + 3(4) = 5       Ta-da!   Now the x's are unhooked from the 1's

                              6x + 12   =  5

                                        6x =  5 - 12

                                             =  -7

                                        x  =  -7/6

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