What is expand (x^2-2y^2)\times e^{x-y} ?

The solution to expand (x^2-2y^2)\times e^{x-y} is e^{x-y}x^2-2e^{x-y}y^2

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expand (x^2-2y^2)\times e^{x-y}

expand

(x^{2} - 2 y^{2}) \cdot e^{x - y}

e^{x - y} x^{2} - 2 e^{x - y} y^{2}

Solution steps

(x^{2} - 2 y^{2}) e^{x - y}

= e^{x - y} (x^{2} - 2 y^{2})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{x - y}, b = x^{2}, c = 2 y^{2}

= e^{x - y} x^{2} - e^{x - y} \cdot 2 y^{2}

= e^{x - y} x^{2} - 2 e^{x - y} y^{2}

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

- 2 x (x^{2} y cos (x^{2} y) + sin (x^{2} y))

\frac{7 x ^{2} - 23 x + 26}{( x + 2 ) ( x - 3 ) ^{2}}

\frac{4 p q ^{4} ( 7 p + 1 )}{5 r}

cos (k x - wt) + cos ((k + d k) x - (w + d w) t)

What is expand (x^2-2y^2)\times e^{x-y} ?
The solution to expand (x^2-2y^2)\times e^{x-y} is e^{x-y}x^2-2e^{x-y}y^2