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

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Scroll down to the bottom for the answer key.

Quiz Answer Key and Fun Facts

Answer:
**100**

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.

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.

Answer:
**2500**

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.

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.

Answer:
**1800**

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.

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.

Answer:
**40000**

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.

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.

Answer:
**125**

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.

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.

Answer:
**4200**

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.

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.

Answer:
**160000**

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.

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.

Answer:
**3600**

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.

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.

Answer:
**100**

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.

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.

Answer:
**10**

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!

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!

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