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

The solution to expand (ln(x)-1)^3 is ln^3(x)-3ln^2(x)+3ln(x)-1

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expand (ln(x)-1)^3

expand

(ln (x) - 1)^{3}

ln^{3} (x) - 3 ln^{2} (x) + 3 ln (x) - 1

Solution steps

(ln (x) - 1)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = ln (x), b = 1

= ln^{3} (x) - 3 ln^{2} (x) \cdot 1 + 3 ln (x) \cdot 1^{2} - 1^{3}

Simplify

ln^{3} (x) - 3 ln^{2} (x) \cdot 1 + 3 ln (x) \cdot 1^{2} - 1^{3} : ln^{3} (x) - 3 ln^{2} (x) + 3 ln (x) - 1

= ln^{3} (x) - 3 ln^{2} (x) + 3 ln (x) - 1

\frac{d ^{2}}{d x ^{2}} ((y) (6 x - 3))

\frac{7 s - 16}{( s - 2 ) ^{2} + 16}

∣ A - B ∣^{2}

\frac{4}{( 2 x ^{8} - 5 ) ^{4}}

\frac{( 18 - ln ( 3 ) ) ( 81 - 3 )}{6558}

What is expand (ln(x)-1)^3 ?
The solution to expand (ln(x)-1)^3 is ln^3(x)-3ln^2(x)+3ln(x)-1