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1. Can x^3+8 be factored? Explain

A. Yes, because x^3 and 8 both share a common factor.
B. No, because x^3 and 8 do not have any common factors.
C. Yes, becahse a sum of cubes can be factored. D. No, becahse a sum of cubes cannot be factored.

2. Determine whether each identity is true or false.

A. a^2-2ab+b^2=(a+b)(a-b)

B. a^2-b^2=(a+b)(a+b)

C. a^2+2ab+b^2=(a+b)(a+b)

D. a^3-b^3=(a-b)(a^2+ab+b)

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Аноним Аноним · Answer 1 · 2020-10-03T23:44:46+02:00

Answer:

1. C. Yes, because a sum of cubes can be factored

2a. false

2b. false

2c. true

2d. false (based on what is written in the equation; refer to step-by-step)

Step-by-step explanation:

1. Both 3 and 8 can be cubed, which is why x^3+8 can be factored (x+2)(x^2-2x+4)

2a. a^2-b^2 can be factored by the perfect square rule, so it should be (a-b)^2

2b. both terms are perfect squares, so you can factor, making it (a+b)(a-b)

2c. You can factor using the perfect square rule, making it (a+b)^2

2d. Most of what is in the equation is true, yet the correct solution would be (a-b)(a^2+ab+b^2)