Quiz Answer Key and Fun Facts
1. In algebra, you learned that (A - B)^2 = A^2 - 2AB + B^2. Use this result to compute the exact value of the following expression:
23^2 - 2 * 23 * 13 + 13^2
2. In algebra, you learn that (A + B)^2 = A^2 + 2AB + B^2. Use this result to compute the exact value of the following expression:
33^2 + 2 * 33 * 17 + 17^2
3. In algebra, you learn that (A + B)(C + D) = AC + AD + BC + BD. Use this result to compute the exact value of the following expression:
13 * 42 + 13 * 18 + 17 * 42 + 17 * 18
4. In algebra, you learn that a difference of squares factors as
A^2 - B^2 = (A - B)(A + B). Use this result to compute the exact value of the following expression:
250^2 - 150^2
5. In algebra, you learn that (A - B)^3 = A^3 - 3A^2B + 3AB^2 - B^3. Use this result to compute the exact value of the following expression:
17^3 - 3 * 17^2 * 12 + 3 * 17 * 12^2 - 12^3
6. You know from algebra how to factor a quadratic polynomial such as
x^2 - 16x + 39. So factor this polynomial, and then let x be a certain number to obtain the exact value of the following expression without any hard work:
73^2 - 16 * 73 + 39
7. We can factor A^4 - 2A^2B^2 + B^4 as (A^2 - B^2)^2 = ((A - B)(A + B))^2. Use this result to compute the exact value of the following expression:
25^4 - 2 * 25^2 * 15^2 + 15^4
8. By multiplying, you can show that (A + B + C)^2 = A^2 + B^2 + C^2 + 2AB + 2AC + 2BC. Use this result to compute the exact value of the following expression:
19^2 + 20^2 + 21^2 + 2*19*20 + 2*19*21 + 2*20*21
9. By multiplying, you can show that (A + B - C)^2 = A^2 + B^2 + C^2 + 2AB - 2AC - 2BC. Using this result, compute the exact value of the following expression:
15^2 + 17^2 + 22^2 + 2*15*17 - 2*15*22 - 2*17*22.
10. In algebra, you learned how to simplify rational expressions, such as
(A^4 - B^4)/(A^3 + AB^2 + BA^2 + B^3). The method was to factor the numerator and denominator, then cancel common factors. Do this, and then use your result to compute the exact value of the following expression:
(85^4 - 75^4)/(85^3 + 85*75^2 + 75*85^2 + 75^3).
Source: Author
rodney_indy
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crisw before going online.
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