Question 93383
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(<font color = "red">5x</font><font color = "purple">-6</font>)(<font color = "blue">5x</font><font color = "green">-6</font>) 

This is called "FOIL" for Firsts, Outers, Inners, Lasts

(<font color = "red">5x</font><font color = "purple">-6</font>)(<font color = "blue">5x</font><font color = "green">-6</font>)

Multiply the FIRSTS, that is, the first red <font color = "red">5x</font> in the 
parentheses on the left by the blue <font color = "blue">5x</font> in the
parentheses on the right, which gives 25x². Write 
this down:

25x²

(<font color = "red">5x</font><font color = "purple">-6</font>)(<font color = "blue">5x</font><font color = "green">-6</font>)

Multiply the OUTERS, that is, the terms on the outer
ends, that is, the red <font color = "red">5x</font> on the far left by the green <font color = "green">-6</font> 
on the far right, which gives -30x. Write this down 
next to the 25x²:

25x²-30x

(<font color = "red">5x</font><font color = "purple">-6</font>)(<font color = "blue">5x</font><font color = "green">-6</font>)

Multiply the INNERS, that is, the terms on the inside, 
that is, the purple <font color = "purple">-6</font> by the blue <font color = "blue">5x</font>, which also gives 
-30x. Write this down next to the other -30x:

25x²-30x-30x

(<font color = "red">5x</font><font color = "purple">-6</font>)(<font color = "blue">5x</font><font color = "green">-6</font>)

Multiply the LASTS, that is, the last purple <font color = "purple">-6</font> in the 
parentheses on the left by the last green <font color = "green">-6</font> in the 
parentheses on the right, which gives +36. Write 
this down next to the -30x:

25x²-30x-30x+36

Now the middle two terms are like terms, so we 
can combine them as -60x:

25x² - 60x + 36.

Edwn</pre>