What is expand A(3(e^xx^2+2xe^x)+(e^{x^4}*4x^3)) ?

The solution to expand A(3(e^xx^2+2xe^x)+(e^{x^4}*4x^3)) is 3Ae^xx^2+6Ae^xx+4Ae^{x^4}x^3

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expand A(3(e^xx^2+2xe^x)+(e^{x^4}*4x^3))

expand

A (3 (e^{x} x^{2} + 2 x e^{x}) + (e^{x^{4}} \cdot 4 x^{3}))

3 A e^{x} x^{2} + 6 A e^{x} x + 4 A e^{x^{4}} x^{3}

Solution steps

A (3 (e^{x} x^{2} + 2 x e^{x}) + (e^{x^{4}} \cdot 4 x^{3}))

= A (3 (e^{x} x^{2} + 2 e^{x} x) + (4 e^{x^{4}} x^{3}))

Apply the distributive law:

a (b + c) = ab + a c

a = A, b = 3 (e^{x} x^{2} + 2 x e^{x}), c = (e^{x^{4}} \cdot 4 x^{3})

= A \cdot 3 (e^{x} x^{2} + 2 x e^{x}) + A (e^{x^{4}} \cdot 4 x^{3})

= 3 A (e^{x} x^{2} + 2 e^{x} x) + A (4 e^{x^{4}} x^{3})

Simplify

3 A (e^{x} x^{2} + 2 e^{x} x) + A (4 e^{x^{4}} x^{3}) : 3 A e^{x} x^{2} + 6 A e^{x} x + 4 A e^{x^{4}} x^{3}

= 3 A e^{x} x^{2} + 6 A e^{x} x + 4 A e^{x^{4}} x^{3}

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

(z - 1 - i) (z - 1 + i)

(L - \frac{t}{2}) (r) (H + \frac{k}{2})^{2}

\frac{1}{s ( s + 1 ) ( s ^{2} + 6 s + 13 )}

\frac{x x ^{2} + 36 \cdot 3 - 2 ( x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

What is expand A(3(e^xx^2+2xe^x)+(e^{x^4}*4x^3)) ?
The solution to expand A(3(e^xx^2+2xe^x)+(e^{x^4}*4x^3)) is 3Ae^xx^2+6Ae^xx+4Ae^{x^4}x^3