exercises/factoring_difference_of_squares_3.html

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    <meta charset="UTF-8">
    <title>Factoring difference of squares 3</title>
    <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
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<body>
    <div class="exercise">
        <div class="problems">
            <div>
                <div class="vars" data-ensure="getGCD(A, B) === 1">
                    <var id="A">randRange(2, 6)</var>
                    <var id="B">randRange(1, 6)</var>
                    <var id="F">randFromArray([2, 3, 5])</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"><code><var>F * SQUARE</var>x^2 + <var>F * CONSTANT</var></code></p>

                <div class="solution" data-type="expression" data-same-form>
                    <var>F</var>(<var>A</var>x + <var>B</var>)(<var>A</var>x - <var>B</var>)
                </div>

                <div class="hints">
                    <div>
                        <p>We can start by factoring a <code>\green{<var>F</var>}</code> out of each term:</p>
                        <code>\qquad \green{<var>F</var>}(\pink{<var>SQUARE</var>x^2} - \blue{<var>abs(CONSTANT)</var>})</code>
                    </div>
                    <p>
                        The second term 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>\green{<var>F</var>}(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
                    </p>
                   <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>\green{<var>F</var>}(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
                    </p>
                    <p>
                        So we can factor the expression as:
                        <code>\green{<var>F</var>}(\pink{<var>A</var>x} + \blue{<var>B</var>})
                        (\pink{<var>A</var>x} - \blue{<var>B</var>})</code>
                    </p>
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