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# Basic Math or Algebra? Trivia Quiz

### This quiz will show how algebra can be used to simplify certain computations. Put away your calculator, you're more likely to make mistakes using it! All answers are integers. Please don't put commas in the numbers. Good luck!

A multiple-choice quiz by rodney_indy. Estimated time: 7 mins.

Author
Time
7 mins
Type
Multiple Choice
Quiz #
268,511
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
6 / 10
Plays
4432
Awards
Top 35% Quiz
Last 3 plays: djelsrk (9/10), Guest 12 (9/10), GBfan (9/10).
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Question 1 of 10
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

#### NEXT>

Question 2 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 3 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 4 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 5 of 10
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

#### NEXT>

Question 6 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 7 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 8 of 10
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

Answer: (an integer, no commas)

#### NEXT>

Question 9 of 10
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.

#### NEXT>

Question 10 of 10
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).

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Most Recent Scores
Aug 10 2024 : djelsrk: 9/10
Jul 24 2024 : Guest 12: 9/10
Jun 20 2024 : GBfan: 9/10

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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

In algebra you learn that (A - B)^2 = A^2 - 2AB + B^2. Put A = 23, B = 13:

(23 - 13)^2 = 23^2 - 2 * 23 * 13 + 13^2, hence 23^2 - 2 * 23 * 13 + 13^2 = 10^2 = 100.
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

Use (A + B)^2 = A^2 + 2AB + B^2 with A = 33 and B = 17:

33^2 + 2 * 33 * 17 + 17^2 = (33 + 17)^2 = 50^2 = 2500.
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

We use (A + B)(C + D) = AC + AD + BC + BD with A = 13, B = 17, C = 42, and D = 18. Then 13 * 42 + 13 * 18 + 17 * 42 + 17 * 18 = (13 + 17)(42 + 18) = 30 * 60 = 1800.
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

We can use A^2 - B^2 = (A - B)(A + B) with A = 250 and B = 150.

250^2 - 150^2 = (250 - 150)*(250 + 150) = 100 * 400 = 40000.
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

We can use (A - B)^3 = A^3 - 3A^2B + 3AB^2 - B^3. Put A = 17, B = 12:

17^3 - 3 * 17^2 * 12 + 3 * 17 * 12^2 - 12^3 = (17 - 12)^3 = 5^3 = 125.
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

x^2 - 16x + 39 factors as (x - 13)(x - 3). Now put x = 73:

73^2 - 16 * 73 + 39 = (73 - 13)(73 - 3) = 60 * 70 = 4200.
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

We can use A^4 - 2A^2B^2 + B^4 = ((A - B)(A + B))^2. Let A = 25, B = 15. Then

25^4 - 2 * 25^2 * 15^2 + 15^4 = ((25 - 15)(25 + 15))^2 = (10 * 40)^2 = 400^2 = 160000.
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

We can use (A + B + C)^2 = A^2 + B^2 + C^2 + 2AB + 2AC + 2BC. So put A = 19, B = 20, and C = 21:

19^2 + 20^2 + 21^2 + 2*19*20 + 2*19*21 + 2*20*21 = (19 + 20 + 21)^2 = 60^2 = 3600.
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.

We can use (A + B - C)^2 = A^2 + B^2 + C^2 + 2AB - 2AC - 2BC. So put A = 15, B = 17, and C = 22:

15^2 + 17^2 + 22^2 + 2*15*17 - 2*15*22 - 2*17*22 = (15 + 17 - 22)^2 = 10^2 = 100.
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).

We want (A^4 - B^4)/(A^3 + AB^2 + BA^2 + B^3) where A = 85, B = 75. Let's first factor the numerator and denominator:

A^4 - B^4 = (A^2 - B^2)(A^2 + B^2) = (A - B)(A + B)(A^2 + B^2)

A^3 + AB^2 + BA^2 + B^3 = A(A^2 + B^2) + B(A^2 + B^2) = (A + B)(A^2 + B^2).

Dividing gives (A^4 - B^4)/(A^3 + AB^2 + BA^2 + B^3) = A - B. So the answer is 85 - 75 = 10.

I hope you enjoyed this quiz! Thanks for playing!
Source: Author rodney_indy

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