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9fa901c @beneater Polynomial exercise name changes and other nits
beneater authored
1 <!DOCTYPE html>
12f5d25 @petercollingridge Change wording of factoring questions
petercollingridge authored
2 <html data-require="math graphie">
cde9e9f @jeresig Re-run the exercises through the updated cleaner.
jeresig authored
3 <head>
e9807ff @jeresig Clean up the exercise files using the new cleaning utility.
jeresig authored
4 <meta charset="UTF-8">
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
5 <title>Factoring difference of squares 1</title>
ac1415e @spicyj Use requirejs for module loading
spicyj authored
6 <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
9fa901c @beneater Polynomial exercise name changes and other nits
beneater authored
7 </head>
8 <body>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
9 <div class="exercise">
10 <div class="problems">
11 <div>
12 <div class="vars">
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
13 <var id="A">randRange(2, 9)</var>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
14 <var id="CONSTANT">-A * A</var>
15 </div>
12f5d25 @petercollingridge Change wording of factoring questions
petercollingridge authored
16
17 <p class="question">
18 Factor the expression below completely. All coefficients should be integers.
19 </p>
20
21 <p class="problem">
22 <span id="question-x"><code>x^2</code></span>
23 <code><span data-if="CONSTANT > 0">+</span><span data-else="">-</span></code>
24 <span id="question-c"><code><var>abs(CONSTANT)</var></code></span>
25 </p>
9fa901c @beneater Polynomial exercise name changes and other nits
beneater authored
26
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
27 <div class="solution" data-type="expression" data-same-form>
28 (x + <var>A</var>)(x - <var>A</var>)
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
29 </div>
9fa901c @beneater Polynomial exercise name changes and other nits
beneater authored
30
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
31 <div class="hints">
12f5d25 @petercollingridge Change wording of factoring questions
petercollingridge authored
32 <div>
33 <p>
34 The expression is in the form <code>\pink{a^2} - \blue{b^2}</code>,
35 which is a difference of two squares so we can factor it as
36 <code>(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
37 </p>
38 <div class="graphie" style="outline: none;">
39 $("#question-x").addClass("hint_pink");
40 $("#question-c").addClass("hint_blue");
41 </div>
42 </div>
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
43 <p>What are the values of <code>\pink{a}</code> and <code>\blue{b}</code>?</p>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
44 <div>
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
45 <p><code>\qquad \pink{a = \sqrt{x^2} = x}</code></p>
46 <p><code>\qquad \blue{b = \sqrt{<var>A * A</var>} = <var>A</var>}</code></p>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
47 </div>
48 <p>
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
49 Use the values we found for <code>\pink{a}</code> and <code>\blue{b}</code>
50 to complete the factored expression,
51 <code>(\pink{a} + \blue{b})(\pink{a} - \blue{b})</code>.
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
52 </p>
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
53 <p>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
54 So we can factor the expression as:
571d54d @petercollingridge Change answer type to expression and tweak hints
petercollingridge authored
55 <code>(\pink{x} + \blue{<var>A</var>})(\pink{x} - \blue{<var>A</var>})</code>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
56 </p>
57 </div>
58 </div>
59 </div>
60 </div>
cde9e9f @jeresig Re-run the exercises through the updated cleaner.
jeresig authored
61 </body>
62 </html>
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