<p><span style="font-size:18px;"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-operations-with-expressions" target="_blank">Operations with Expressions Exercise</a></span></p>
<p><span style="font-size:18px;"><strong>Note</strong>: many students have been confused and asked us (about 4 minutes into the video) why x = 0 does not work, when it supposedly does in the final expression. The reason is that you need to look at the <strong>initial</strong> expression instead, where x = 0 won't work. Formally, the domain does not change when you simplify the expression (it's OK if you are unfamiliar with the "domain" word - we'll introduce this term later on in the course).</span></p><p>We can apply our arithmetic operations on algebraic expressions too!</p>
<p>Addition and Subtraction are not too bad:</p>
<ul>
<li>$5x+3x=8x$</li>
<li>$10r^3 - 3r^3 = 7r^3$</li>
</ul>
<p>Note that you can only add or subtract terms that share variables with the same exponents.</p>
<p>Multiplication is very easy, you don't need to worry about like terms, just multiply everything together.</p>
<p>$8y^2(2y^3)7z = 112y^5z$</p>
<p>Division is tricky, there's a few things to watch out for here. Often, you need to factorize:</p>
<ol>
<li>$\frac{6x^2+9x}{12x-5x^2}$ can be factorized into $\frac{3x(2x+3)}{3x(4-5x)}$ </li>
<li>We can then cancel the $3x$ from the top and bottom into $\frac{2x+3}{4-5x}$.</li>
</ol>
<p>The result doesn't seem that simple, but it's still better than what we started with.</p>
<p>There's a catch here though, remember the golden rule of fractions? $x$ cannot be anything that causes the denominator to be $0$, because if you divide by $0$, you never know what may happen...</p>