What is expand xe^{6xy}(ye^{6xy}+x) ?

The solution to expand xe^{6xy}(ye^{6xy}+x) is e^{12xy}xy+e^{6xy}x^2

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expand xe^{6xy}(ye^{6xy}+x)

expand

x e^{6 x y} (y e^{6 x y} + x)

e^{12 x y} x y + e^{6 x y} x^{2}

Solution steps

x e^{6 x y} (y e^{6 x y} + x)

= e^{6 x y} x (e^{6 x y} y + x)

Apply the distributive law:

a (b + c) = ab + a c

a = x e^{6 x y}, b = y e^{6 x y}, c = x

= x e^{6 x y} y e^{6 x y} + x e^{6 x y} x

= e^{6 x y} e^{6 x y} x y + e^{6 x y} xx

Simplify

e^{6 x y} e^{6 x y} x y + e^{6 x y} xx : e^{12 x y} x y + e^{6 x y} x^{2}

= e^{12 x y} x y + e^{6 x y} x^{2}

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a cos (ω t - k x) + a cos (ω t - k (x + δ x))

e (\frac{- π + 1 + π ^{2}}{π ^{2} - π} - 1)

\frac{k ( s + 1 )}{s ^{2} ( s + 10 ) ( s + 100 )}

What is expand xe^{6xy}(ye^{6xy}+x) ?
The solution to expand xe^{6xy}(ye^{6xy}+x) is e^{12xy}xy+e^{6xy}x^2