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<!DOCTYPE html>
<html data-require="math graphie">
<head>
<meta charset="UTF-8">
<title>Factoring difference of squares 2</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars" data-ensure="getGCD(A, B) === 1">
<var id="A">randRange(2, 9)</var>
<var id="B">randRange(1, 9)</var>
<var id="SQUARE">A * A</var>
<var id="CONSTANT">-B * B</var>
</div>
<p class="question">
Factor the expression below completely. All coefficients should be integers.
</p>
<p class="problem">
<span id="question-x"><code><var>SQUARE</var>x^2</code></span>
<code><span data-if="CONSTANT > 0">+</span><span data-else="">-</span></code>
<span id="question-c"><code><var>abs(CONSTANT)</var></code></span>
</p>
<div class="solution" data-type="expression" data-same-form>
(<var>A</var>x + <var>B</var>)(<var>A</var>x - <var>B</var>)
</div>
<div class="hints">
<div>
<p>
The expression is of the form <code>\pink{a^2} - \blue{b^2}</code>,
which is a difference of two squares so we can factor it as
<code>(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
</p>
<div class="graphie" style="outline: none;">
$("#question-x").addClass("hint_pink");
$("#question-c").addClass("hint_blue");
</div>
</div>
<p>What are the values of <code>\pink{a}</code> and <code>\blue{b}</code>?</p>
<div>
<p><code>\qquad \pink{a = \sqrt{<var>SQUARE</var>x^2} = <var>A</var>x}</code></p>
<p><code>\qquad \blue{b = \sqrt{<var>B * B</var>} = <var>B</var>}</code></p>
</div>
<p>
Use the values we found for <code>\pink{a}</code> and <code>\blue{b}</code>
to complete the factored expression,
<code>(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
</p>
<p>
So we can factor the expression as:
<code>(\pink{<var>A</var>x} + \blue{<var>B</var>})(\pink{<var>A</var>x} - \blue{<var>B</var>})</code>
</p>
</div>
</div>
</div>
</div>
</body>
</html>
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