Algebraic identities

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Last updated 9:27 AM on 6/5/26
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33 Terms

1
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(a + b)²

a² + 2ab + b²

2
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(a - b)²

a² - 2ab + b²

3
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(a + b)(a - b)

a² - b²

4
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(a + b)³

a³ + 3a²b + 3ab² + b³

5
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(a - b)³

a³ - 3a²b + 3ab² - b³

6
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a³ + b³

(a + b)(a² - ab + b²)

7
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a³ - b³

(a - b)(a² + ab + b²)

8
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a³ + b³ + 3ab(a + b)

(a + b)³

9
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a³ - b³ - 3ab(a - b)

(a - b)³

10
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(a + b)³ - 3ab(a + b)

a³ + b³

11
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(a - b)³ + 3ab(a - b)

a³ - b³

12
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(a + b + c)²

a² + b² + c² + 2ab + 2bc + 2ca

13
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a³ + b³ + c³ - 3abc

(a + b + c)(a² + b² + c² - ab - bc - ca)

14
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a³ + b³ + c³ - 3abc

(a + b + c)[(a + b + c)² - 3(ab + bc + ca)]

15
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a³ + b³ + c³ - 3abc

½(a + b + c)[(a - b)² + (b - c)² + (c - a)²]

16
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a + b + c = 0

a³ + b³ + c³ = 3abc

17
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(a + b)² + (a - b)²

2(a² + b²)

18
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(a + b)² - (a - b)²

4ab

19
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(x + a)(x + b)

x² + (a + b)x + ab

20
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(x - a)(x - b)

x² - (a + b)x + ab

21
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(x + a)(x - b)

x² + (a - b)x - ab

22
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(x + 1/x)²

x² + 1/x² + 2

23
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x² + 1/x²

(x + 1/x)² - 2

24
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(x - 1/x)²

x² + 1/x² - 2

25
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x² + 1/x²

(x - 1/x)² + 2

26
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x³ + 1/x³

(x + 1/x)³ - 3(x + 1/x)

27
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x³ - 1/x³

(x - 1/x)³ + 3(x - 1/x)

28
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x + 1/x = 1

x² + 1/x² = -1

29
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x + 1/x = 1

x³ + 1/x³ = -2

30
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x + 1/x = 2

x² + 1/x² = 2

31
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x + 1/x = 2

x³ + 1/x³ = 2

32
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x + 1/x = 3

x² + 1/x² = 7

33
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x + 1/x = 3

x³ + 1/x³ = 18