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

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

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

expand

(ln (x) + 1) (ln (x) + 2)

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

Solution steps

(ln (x) + 1) (ln (x) + 2)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = ln (x), b = 1, c = ln (x), d = 2

= ln (x) ln (x) + ln (x) \cdot 2 + 1 \cdot ln (x) + 1 \cdot 2

= ln (x) ln (x) + 2 ln (x) + 1 \cdot ln (x) + 1 \cdot 2

Simplify

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

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

\frac{( s + 2.847050174 ) ^{2}}{s}

(- 4 v, - 1, 2 u + 1) (0, 2, 1)

(v, u + v, 2 u^{2} - 2 v^{2}) \cdot (- 2 u - 4 v, 4 v, 1)

\frac{\partial}{\partial u} ((y) (uv - z (y, u, v)))

\frac{( - 2 x - 3 x ^{2} ) ( 4 - x ^{2} - x ^{3} )}{h}

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