SOLUTION: (x+6)(4x-3)

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Question 984700: (x+6)(4x-3)
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You have two binomials (meaning two terms). Use FOIL, which stands for First, Outside, Inside, Last.

First:      x  and  4x   x times 4x is 4x²

Outside:    x  and  -3   x times -3 is -3x

Inside:     6  and  4x   6 times 4x is 24x

Last:       6  and  -3   6 times -3 is -18

Then add up the results:   4x² - 3x + 24x - 18

Almost done.  The two middle terms are "like" terms, so we can add them.  -3 + 24 is 21, so your final result is:

                           4x² + 21x -18

Note that you don't have to do the multiplications in that exact order. You could do Last, Outside, First, Inside if you wanted to. But LOFI doesn't spell anything, so it is harder to remember than FOIL.

Why This Works

Remember the Distributive Property?



for all real numbers, a, b, and c.

Well what if and ? Couldn't you substitute into the general form of the Distributive Property and get:



And then, in the right hand side of the equation, distribute 4x across x + 6 and (-3) across x + 6 giving you the same result as the FOIL process?



John

My calculator said it, I believe it, that settles it

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Use distributive property and combine like-terms if any occur. If your polynomial factors have more than two terms each, then a lattice type form of multiplication would make the work easier, and more organized. This way, you simply fill-in cells, and then identify the like-terms and combine, ... but you can still use distributive property; it is just more difficult to use if the factors are too many terms.

Know that when you perform regular multidigit long multiplication for power-of-ten regular numbers, you are essentially doing something like a lattice method. The often included act of "carrying" condenses the process and hides the lattice characteristic about the method from the student (or whoever is doing the multiplication).
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