-------------------------------------------------------
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
-
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
-
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.
-
Como say: [ x - 1 ] [ x² - 2x + 1 ]
x³ - 2x² + x - x² + 2x - 1
x³ - 3x² + 3x - 1
-
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
-
Kt Skycat say: x>1
-
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
-
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.
-
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
-
D.W. say: (a+b)³ = a³ + 3a²b + 3ab² + b³
Just substitute.
-
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
-
Pinkgreen say: (x-1)^3=
(x-1)(x-1)^2=
(x-1)(x^2-2x+1)=
x^3-3x^2+3x-1
-