<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-simplifying-algebraic-expressions-1" target="_blank">Simplifying Algebraic Expressions 1 Exercise</a></span></p><p>We can make use of all the concepts learned so far to make algebraic expressions a lot simpler. Here are 5 scenarios you might encounter.</p>
<p><strong>Scenario 1: </strong></p>
<p>Sometimes we just multiply variables.</p>
<p>$(a)(a)(a) = a^3$</p>
<p>Other times, we need to factor stuff out:</p>
<p>$\frac{3z-6y}{3}$ can be simplified by factoring out the $3$: $\frac{3(z-2y)}{3}$ becomes $z-2y$.</p>
<p><strong>Scenario 2:</strong></p>
<p>Sometimes, we can make use of PEMDAS rules:</p>
<p>$3(b+(4b-2b))-(5b-3b)$ </p>
<p>We can just evaluate the brackets to clean up this messy expression:</p>
<p>1. $3(b+2b) - 2b$<br />
2. $3(3b) - 2b$<br />
3. $9b-2b$<br />
4. $7b$</p>
<p><strong>Scenario 3:</strong></p>
<p>If we have a fraction with the same numerator and denominator, we can simplify it to $1$, provided that the denominator is not $0$.</p>
<p>$\frac{r-4}{r-4}$ is $1$, as long as $r$ does not equal $4$.</p>
<p>$\frac{|x|}{x}$ would be $1$ or $-1$ depending on whether $x$ is positive or negative, we still need to ensure $x$ is not equal to $0$.</p>
<p><strong>Scenario 4:</strong></p>
<p>We can also make use of our identities to help us simplify.</p>
<p>$x(x-1)(x+1)$ into $x(x^2-1)$ and then into $x^3-x$. Keep an eye out for this one, because it pops up quite a lot!</p>
<p><strong>Scenario 5:</strong></p>
<p>We might also need to set a common denominator to add up fractions, just like arithmetic:</p>
<p>$\frac{y+3}{3}+\frac{y+3}{2}$ becomes $\frac{2(y+3)}{6}+\frac{3(y+3)}{6}$ and now we can add up the top into $\frac{5(y+3)}{6}$.</p>