What is (x-1)^3?
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What is (x-1)^3?

[From: ] [author: ] [Date: 17-04-14] [Hit: ]
you can use the shortcut. But for this small case, you can easily do it by expanding as shown above.D.W.Just substitute.......
What is (x-1)^3?

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answers:
m say: You can find it this way:
(x-1)*(x-1)*(x-1) = (x^2 -2x+1)(x-1) = x^3 -2x^2 + x - x^2 + 2x - 1 = x^3 -3x^2 +3x -1
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Deepak Suwalka say: Use the property

(a - b)³ = a³ - 3a²b + 3ab² - b³

Similarly,

(x - 1)³ = x³ - 3x²1 + 3x1² - 1³

= x³ - 3x² + 3x - 1
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Nzewi Ernest Kenechukwu say: (x - 1)³

=> Using the concept of Pascal's Triangle for the power of 3: (1 - 3 - 3 - 1); the binomial expansion of the expression above is expanded as

x³ - 3x² + 3x - 1 ...Ans.
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Como say: [ x - 1 ] [ x² - 2x + 1 ]
x³ - 2x² + x - x² + 2x - 1
x³ - 3x² + 3x - 1
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Krishnamurthy say: (x - 1)^3
= (x - 1)(x - 1)^2
= (x - 1)(x^2 - 2x + 1)
= x^3 - 2x^2 + x - x^2 + 2x - 1
= x^3 - 3x^2 + 3x - 1
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Kt Skycat say: x>1
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Brainard say: (x-1)^3 = (x - 1)(x^2 - 2x + 1)

= x(x^2 - 2x + 1) - 1(x^2 - 2x + 1)

= x^3 - 2x^2 + x - x^2 + 2x - 1

= x^3 - 3x^2 + 3x - 1
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Puzzling say: Original expression:
(x - 1)^3

Expand it by multiplying by itself 3 times:
(x - 1)(x - 1)(x - 1)

FOIL out a pair of terms:
(x - 1)(x² - 2x + 1)

Distribute:
x(x² - 2x + 1) - 1(x² - 2x + 1)
x^3 - 2x² + x - x² + 2x - 1

Combine like terms:
x^3 - 3x² + 3x - 1

P.S. If you are familiar with binomial expansion, you can use the shortcut. But for this small case, you can easily do it by expanding as shown above.
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sioieng say: (x - 1)³ = x³ - 3x² + 3x - 1

(x - 1)³
=(x - 1)(x - 1)²
= (x - 1)(x² - 2x + 1)
= x(x² - 2x + 1) - (x² - 2x + 1)
= x³ - 2x² + x - x² + 2x - 1)
= x³ - 3x² + 3x - 1
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D.W. say: (a+b)³ = a³ + 3a²b + 3ab² + b³
Just substitute.
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Polyhymnio say: Use the binomial theorem

(x - 1)³ = 3C0 x³(-1)° + 3C1 x²(-1)¹ + 3C2 x¹(-1)² + 3C3 x°(-1)³ =

x³ - 3x² + 3x - 1
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Pinkgreen say: (x-1)^3=
(x-1)(x-1)^2=
(x-1)(x^2-2x+1)=
x^3-3x^2+3x-1
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