What is expand [y(4x+y)-2(x^{(2)}-y)]*(-2)ln|y| ?

The solution to expand [y(4x+y)-2(x^{(2)}-y)]*(-2)ln|y| is -8yxln|y|-2y^2ln|y|+4x^2ln|y|-4yln|y|

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expand [y(4x+y)-2(x^{(2)}-y)]*(-2)ln|y|

expand

[y (4 x + y) - 2 (x^{(2)} - y)] \cdot (- 2) ln ∣ y ∣

- 8 y x ln ∣ y ∣ - 2 y^{2} ln ∣ y ∣ + 4 x^{2} ln ∣ y ∣ - 4 y ln ∣ y ∣

Solution steps

(y (4 x + y) - 2 (x^{2} - y)) (- 2) ln ∣ y ∣

Remove parentheses:

(- a) = - a

= - (y (4 x + y) - 2 (x^{2} - y)) \cdot 2 ln ∣ y ∣

Expand

y (4 x + y) - 2 (x^{2} - y) : 4 y x + y^{2} - 2 x^{2} + 2 y

= - 2 ln ∣ y ∣ (y^{2} + 4 y x + 2 y - 2 x^{2})

= - 2 ln ∣ y ∣ (4 y x + y^{2} - 2 x^{2} + 2 y)

Distribute parentheses

= (- 2 ln ∣ y ∣) \cdot 4 y x + (- 2 ln ∣ y ∣) y^{2} + (- 2 ln ∣ y ∣) (- 2 x^{2}) + (- 2 ln ∣ y ∣) \cdot 2 y

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 2 \cdot 4 y x ln ∣ y ∣ - 2 y^{2} ln ∣ y ∣ + 2 \cdot 2 x^{2} ln ∣ y ∣ - 2 \cdot 2 y ln ∣ y ∣

Simplify

- 2 \cdot 4 y x ln ∣ y ∣ - 2 y^{2} ln ∣ y ∣ + 2 \cdot 2 x^{2} ln ∣ y ∣ - 2 \cdot 2 y ln ∣ y ∣ : - 8 y x ln ∣ y ∣ - 2 y^{2} ln ∣ y ∣ + 4 x^{2} ln ∣ y ∣ - 4 y ln ∣ y ∣

= - 8 y x ln ∣ y ∣ - 2 y^{2} ln ∣ y ∣ + 4 x^{2} ln ∣ y ∣ - 4 y ln ∣ y ∣

(\frac{x ^{2}}{2} + \frac{3}{x})^{6}

\frac{e ^{x} - 3}{( e ^{x} - 5 ) ( e ^{x} - 7 ) ( e ^{x} + 1 )}

\frac{5 ( 1 - x )}{( x + 1 ) ^{3}}

\frac{s ( s ^{2} - 1 )}{s ^{3} + 2 s - 4}

(t - 1) e^{2 t}

What is expand [y(4x+y)-2(x^{(2)}-y)]*(-2)ln|y| ?
The solution to expand [y(4x+y)-2(x^{(2)}-y)]*(-2)ln|y| is -8yxln|y|-2y^2ln|y|+4x^2ln|y|-4yln|y|