Question 569735
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Remember the word FOIL. F for FIRSTS, O for OUTERS, I for INNERS, 
and L for LASTS.

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The FIRSTS are the <font color="red">7y²</font> and the <font color="red">y²</font>

(<font color="red">7y²</font>+x)(<font color="red">y²</font>-2x)

That's because the <font color="red">7y²</font> comes FIRST in the (<font color="red">7y²</font>+x)
and the <font color="red">y²</font> comes FIRST in the (<font color="red">y²</font>-2x)

So we multiply them together

7y²·y² = 7y<sup>4</sup>

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The OUTERS are the <font color="red">7y²</font> and the <font color="red">-2x</font>

(<font color="red">7y²</font>+x)(y²<font color="red">-2x</font>)

That's because the <font color="red">7y²</font> and the <font color="red">-2x</font> are on the OUTSIDE
(That is they are the farthest OUT from each other)

So we multiply them together

7y²·-2x = -14xy²

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The INNERS are the <font color="red">+x</font> and the <font color="red">y²</font>

(7z²<font color="red">+x</font>)(<font color="red">y²</font>-2x)

That's because the <font color="red">+x</font> and the <font color="red">y²</font> are on the INSIDE
(That is they are in the middle)

So we multiply them together

+x·y² = +xy²

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The LASTS are the <font color="red">+x</font> and the <font color="red">-2x</font>

(7y²<font color="red">+x</font>)(y²<font color="red">-2x</font>)

That's because the <font color="red">+x</font> comes LAST in the (7y²<font color="red">+x</font>)
and the <font color="red">-2x</font> comes LAST in the (y²<font color="red">-2x</font>)

So we multiply them together

+x·-2x = -2x²

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Write down the four terms from above for FIRSTS, OUTERS, INNERS, and LASTS:

7y<sup>4</sup>-14xy²+xy²-2x²

The two middle terms are like terms, so they will combine as -13xy²

Answer: 7y<sup>4</sup>-13xy²-2x² 

Edwin</pre>