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<title>Factoring difference of squares 1</title>
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<div class="exercise">
<div class="problems">
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<div class="vars">
<var id="A">randRange(2, 9)</var>
<var id="CONSTANT">-A * A</var>
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<p class="question">
Factor the expression below completely. All coefficients should be integers.
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<p class="problem">
<span id="question-x"><code>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>
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<div class="solution" data-type="expression" data-same-form>
(x + <var>A</var>)(x - <var>A</var>)
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<div class="hints">
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<p>
The expression is in 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>.
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<p>What are the values of <code>\pink{a}</code> and <code>\blue{b}</code>?</p>
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<p><code>\qquad \pink{a = \sqrt{x^2} = x}</code></p>
<p><code>\qquad \blue{b = \sqrt{<var>A * A</var>} = <var>A</var>}</code></p>
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<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>.
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<p>
So we can factor the expression as:
<code>(\pink{x} + \blue{<var>A</var>})(\pink{x} - \blue{<var>A</var>})</code>
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