Question 165482
<font size = 7 color = "red"><b>Edwin's solution:</b></font>

Use FOIL to multiply:
<pre><font size = 4 color = "indigo"><b>

(3x – 8)(x – 7)

You can make four pairs out of that:

The F in "FOIL" stands for "FIRSTS"
The red ones below are the Firsts

(<font color = "red">3x</font> – 8)(<font color = "red">x</font> – 7)

That's because the 3x comes FIRST in the (3x - 8)
and x comes first in (x - 7)

So when we multiply the FIRSTS we get (3x)(x) or 3x<sup>2</sup>

-----------------

The O in "FOIL" stands for "OUTERS"
The red ones below are the Outers:

(<font color = "red">3x</font> – 8)(x <font color = "red">– 7</font>)

That's because the 3x is on the extreme left and
-7 is on the extreme right.  So they are said to
be on the outside.

So when we multiply the OUTERS we get (3x)(-7) or -21x.

-----------------
 
The I in "FOIL" stands for "INNERS"
The red ones below are the INNERS:

(3x <font color = "red">– 8</font>)(<font color = "red">x</font> – 7)

That's because the -8 and the x are in
the middle.  So they are said to
be on the INside.

So when we multiply the INNERS we get (-8)(x) or -8x.

---------------

The L in "FOIL" stands for "LASTS"
The red ones below are the Lasts

(3x <font color = "red">– 8</font>)(x <font color = "red">– 7</font>)

That's because the -8 comes LAST in the (3x - 8)
and -7 comes LAST in (x - 7)

When we multiply the LASTS we get (-8)(-7) or +56.

So when we write out what we have:

FIRSTS:  3x<sup>2</sup> 
OUTERS:  -21x
INNERS:  -8x
LASTS:   +56

So we get 

3x<sup>2</sup>-21x-8x+56

The terms -21x and -8x then combine to give -29x, and so we
have as a final answer:

3x<sup>2</sup>-29x+56
 
Edwin</pre>