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<!DOCTYPE html>
<html data-require="math">
<head>
<meta charset="UTF-8" />
<title>Factoring difference of squares 1</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars">
<var id="A">randRange( 2, 9 )</var>
<var id="SQUARE">1</var>
<var id="CONSTANT">-A * A</var>
</div>
<div>
<p class="question">
Factor the following expression:
</p>
<p>
<code>x^2 + <var>CONSTANT</var></code>
</p>
</div>
<div class="solution" data-type="set">
<div class="set-sol" data-type="regex">^\s*\(\s*[xX]\s*\+\s*<var>abs( A )</var>\s*\)\s*\(\s*[xX]\s*[-\u2212]\s*<var>abs( A )</var>\s*\)\s*$</div>
<div class="set-sol" data-type="regex">^\s*\(\s*[xX]\s*[-\u2212]\s*<var>abs( A )</var>\s*\)\s*\(\s*[xX]\s*\+\s*<var>abs( A )</var>\s*\)\s*$</div>
<div class="input-format"><span class="entry"></span></div>
<div class="example">a factored expression, like <b>(x+1)(x+2)</b></div>
</div>
<div class="hints">
<p>
The expression is in the form <code>\color{<var>PINK</var>}{a^2} - \color{<var>BLUE</var>}{b^2}</code>,
which is a difference of two squares so we can factor it as
<code>(\color{<var>PINK</var>}{a} + \color{<var>BLUE</var>}{b})
(\color{<var>PINK</var>}{a} - \color{<var>BLUE</var>}{b})</code>.
</p>
<p>
What are the values of <code class="hint_pink">a</code> and <code class="hint_blue">b</code>?
</p>
<div>
<p><code class="hint_pink">\qquad a = x</code></p>
<p><code class="hint_blue">\qquad b = \sqrt{<var>A * A</var>} = <var>A</var></code></p>
</div>
<p>
Use the values we found for <code class="hint_pink">a</code> and <code class="hint_blue">b</code>
to complete the factored expression,
<code>(\color{<var>PINK</var>}{a} + \color{<var>BLUE</var>}{b})
(\color{<var>PINK</var>}{a} - \color{<var>BLUE</var>}{b})</code>.
</p>
<p class="final_answer">
So we can factor the expression as:
<code>(\color{<var>PINK</var>}{x} + \color{<var>BLUE</var>}{<var>A</var>})
(\color{<var>PINK</var>}{x} - \color{<var>BLUE</var>}{<var>A</var>})</code>
</p>
</div>
</div>
</div>
</div>
</body>
</html>
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