What is expand ((3ln(6)-5)^2)/2 ?

The solution to expand ((3ln(6)-5)^2)/2 is 25/2+(9ln^2(6))/2-15ln(6)

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expand ((3ln(6)-5)^2)/2

expand

\frac{( 3 ln ( 6 ) - 5 ) ^{2}}{2}

\frac{25}{2} + \frac{9 ln ^{2} ( 6 )}{2} - 15 ln (6)

Solution steps

\frac{( 3 ln ( 6 ) - 5 ) ^{2}}{2}

(3 ln (6) - 5)^{2} = 9 ln^{2} (6) - 30 ln (6) + 25

= \frac{9 ln ^{2} ( 6 ) - 30 ln ( 6 ) + 25}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{9 ln ^{2} ( 6 ) - 30 ln ( 6 ) + 25}{2} = \frac{9 ln ^{2} ( 6 )}{2} - \frac{30 ln ( 6 )}{2} + \frac{25}{2}

= \frac{9 ln ^{2} ( 6 )}{2} - \frac{30 ln ( 6 )}{2} + \frac{25}{2}

Divide the numbers:

\frac{30}{2} = 15

= \frac{9 ln ^{2} ( 6 )}{2} - 15 ln (6) + \frac{25}{2}

Group like terms

= \frac{25}{2} + \frac{9 ln ^{2} ( 6 )}{2} - 15 ln (6)

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What is expand ((3ln(6)-5)^2)/2 ?
The solution to expand ((3ln(6)-5)^2)/2 is 25/2+(9ln^2(6))/2-15ln(6)