What is expand 5(x^2+y^2)e^{y^2-x^2} ?

The solution to expand 5(x^2+y^2)e^{y^2-x^2} is 5e^{y^2-x^2}x^2+5e^{y^2-x^2}y^2

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expand 5(x^2+y^2)e^{y^2-x^2}

expand

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

5 e^{y^{2} - x^{2}} x^{2} + 5 e^{y^{2} - x^{2}} y^{2}

Solution steps

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

= 5 e^{y^{2} - x^{2}} (x^{2} + y^{2})

Apply the distributive law:

a (b + c) = ab + a c

a = 5 e^{y^{2} - x^{2}}, b = x^{2}, c = y^{2}

= 5 e^{y^{2} - x^{2}} x^{2} + 5 e^{y^{2} - x^{2}} y^{2}

\frac{a ^{2} + 4 a + 4}{( 3 a + 3 b ) ( a + b )}

\frac{3 x ^{2} + 1}{( x + 2 ) ^{3}}

- \frac{6 ( u ^{2} - 2 )}{( u ^{2} + 2 ) ^{2}}

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

sin (x) ln (x) (2 x - 1)

What is expand 5(x^2+y^2)e^{y^2-x^2} ?
The solution to expand 5(x^2+y^2)e^{y^2-x^2} is 5e^{y^2-x^2}x^2+5e^{y^2-x^2}y^2