<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-foil-first-outside-inside-last">FOIL (First, Outside, Inside, Last) Exercise</a></span></p><p>This is a nifty system with an even niftier acronym that makes it easy to multiply polynomials with 2 terms.</p>
<p>$(a+b)(c+d)$</p>
<p>The FOIL method helps us remember to multiply:</p>
<ul>
<li><strong>F</strong>irst terms: $a \times c = ac$</li>
<li><strong>O</strong>uter terms: $a \times d = ad$</li>
<li><strong>I</strong>nner terms: $b \times c = bc$</li>
<li><strong>L</strong>ast terms: $b \times d = bd$</li>
</ul>
<p>Putting it all together:</p>
<p>$(a+b)(c+d) = ac + ad + bc + bd$</p>
<p>Let's look at another example:</p>
<p>$(2x + 3)(x + 4)$</p>
<p>Using FOIL:</p>
<ul>
<li><strong>F</strong>irst terms: $2x \times x = 2x^2$</li>
<li><strong>O</strong>uter terms: $2x \times 4 = 8x$</li>
<li><strong>I</strong>nner terms: $3 \times x = 3x$</li>
<li><strong>L</strong>ast terms: $3 \times 4 = 12$</li>
</ul>
<p>Putting it all together:</p>
<p>$(2x + 3)(x + 4) = 2x^2 + 8x + 3x + 12$</p>
<p>Often, after doing <span style="color:#27ae60;">FOIL</span>, you can combine like terms to clean up a bit more:</p>
<p>$2x^2 + 11x + 12$</p>
<p>The <span style="color:#27ae60;">FOIL</span> method is a handy way to keep track of all the terms when multiplying binomials!</p>