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

The solution to expand (x^3-5x^2)ln(x^3+6x^2+5x) is x^3ln(x^3+6x^2+5x)-5x^2ln(x^3+6x^2+5x)

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expand (x^3-5x^2)ln(x^3+6x^2+5x)

expand

(x^{3} - 5 x^{2}) ln (x^{3} + 6 x^{2} + 5 x)

x^{3} ln (x^{3} + 6 x^{2} + 5 x) - 5 x^{2} ln (x^{3} + 6 x^{2} + 5 x)

Solution steps

(x^{3} - 5 x^{2}) ln (x^{3} + 6 x^{2} + 5 x)

= ln (x^{3} + 6 x^{2} + 5 x) (x^{3} - 5 x^{2})

Apply the distributive law:

a (b - c) = ab - a c

a = ln (x^{3} + 6 x^{2} + 5 x), b = x^{3}, c = 5 x^{2}

= ln (x^{3} + 6 x^{2} + 5 x) x^{3} - ln (x^{3} + 6 x^{2} + 5 x) \cdot 5 x^{2}

= x^{3} ln (x^{3} + 6 x^{2} + 5 x) - 5 x^{2} ln (x^{3} + 6 x^{2} + 5 x)

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

\frac{2 ( 54 - 4 2 )}{9}

R^{3} u (2, - 3, 4) v (- 5, 1, 0) w (4, 2, 1)

\frac{12 ( - 243 x ^{2} - 216 x - 8 )}{( 9 x ^{2} + 8 x + 8 ) ^{3}}

\frac{2 x - 1}{( x + 1 ) ^{2}}

What is expand (x^3-5x^2)ln(x^3+6x^2+5x) ?
The solution to expand (x^3-5x^2)ln(x^3+6x^2+5x) is x^3ln(x^3+6x^2+5x)-5x^2ln(x^3+6x^2+5x)