What is expand (ln(x))(x^2(3ln(x)+1)) ?

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

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expand (ln(x))(x^2(3ln(x)+1))

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = ln (x) x^{2}, b = 3 ln (x), c = 1

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

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

Simplify

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

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

(6 a^{3} + 2 ab - 8 b e^{2}) (3 a - 2 b)

36 (4 - π) c m^{2}

B (1, - 4) y C (- 3, 1)

(\frac{1}{8}) (- 4 x + 2 e^{x} + 5 e^{- 2 x} - \frac{12}{e ^{x}})

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

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