Question 153362
Can you please help me expand this set of numbers?
(3x-5)(2x+7)

<pre><font size = 5><b>
Remember the word "FOIL"

The F stands for FIRST.  
The FIRST term in (3x-5) is the 3x.
The FIRST term in (2x+7) is the 2x.

So the FIRSTS are in red below:

(<font color = "red">3x</font>-5)(<font color = "red">2x</font>+7)

Multiply them together and get (<font color = "red">3x</font>)(<font color = "red">2x</font>) = <font color = "red">6x²</font>

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The O stands for OUTERS.  
The OUTER terms are in green below:

(<font color = "green">3x</font>-5)(2x<font color = "green">+7</font>)

Notice that they are on the OUTSIDE.

Multiply them together and get (<font color = "green">3x</font>)(<font color = "green">+7</font>) = <font color = "green">+21x</font>

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The I stands for INNERS.  
The INNER terms are in purple below:

(3x<font color = "indigo">-5</font>)(<font color = "indigo">2x</font>+7)

Notice that they are on the INSIDE.

Multiply them together and get (<font color = "indigo">-5</font>)(<font color = "indigo">2x</font>) = <font color = "indigo">-10x</font>


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The L stands for LASTS.  
The LAST term in (3x-5) is the -5.
The LAST term in (2x+7) is the +7.

So the LASTS are in blue below:

(3x<font color = "blue">-5</font>)(2x<font color = "blue">+7</font>)

Multiply them together and get (<font color = "blue">-5</font>)(<font color = "blue">+7</font>) = <font color = "blue">-35</font>

Now we write them in that order <font color = "red">F</font><font color = "green">O</font><font color = "indigo">I</font><font color = "blue">L</font>

<font color = "red">6x²</font><font color = "green">+21x</font><font color = "indigo">-10x</font><font color = "blue">-35</font>

Now the middle two terms will combine and we end up with:

6x²+11x-35

Edwin</pre>