Mulțimea R, operații algebrice, ordonarea numerelor reale Flashcards

1
Q

Ce fel de structură are R în raport cu adunarea și înmulțirea?

A

O structură de corp comutativ.
(R, +, *) este corp comutativ

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2
Q

(a + b)^2

A

a^2 + 2ab + b^2

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3
Q

a^2 + 2ab + b^2

A

(a + b)^2

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4
Q

(a - b)^2

A

a^2 - 2ab + b^2

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5
Q

a^2 - 2ab + b^2

A

(a - b)^2

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6
Q

a^2 - b^2

A

(a - b)(a + b)

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7
Q

(a - b)(a + b)

A

a^2 - b^2

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8
Q

(a + b)^3

A

a^3 + 3a^2b + 3ab^2 + b^3

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9
Q

a^3 + 3a^2b + 3ab^2 + b^3

A

(a + b)^3

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10
Q

(a - b)^3

A

a^3 - 3a^2b + 3ab^2 - b^3

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11
Q

a^3 - 3a^2b + 3ab^2 - b^3

A

(a - b)^3

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12
Q

a^3 + b^3

A

(a + b)(a^2 - ab + b^2)

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13
Q

(a + b)(a^2 - ab + b^2)

A

a^3 + b^3

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14
Q

a^3 - b^3

A

(a - b)(a^2 + ab + b^2)

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15
Q

(a - b)(a^2 + ab + b^2)

A

a^3 - b^3

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16
Q

Ce fel de relație este <=?

A

De ordine, R fiind o mulțime total ordonată.
(R; <=) mulțime total ordonată

17
Q

a^2 + b^2

A

(a + b)^2 - 2ab

18
Q

(a + b)^2 - 2ab

A

a^2 + b^2