What is expand (e^x+xe^x)(x^2+e^x) ?

The solution to expand (e^x+xe^x)(x^2+e^x) is e^xx^2+e^{2x}+e^xx^3+e^{2x}x

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expand (e^x+xe^x)(x^2+e^x)

expand

(e^{x} + x e^{x}) (x^{2} + e^{x})

e^{x} x^{2} + e^{2 x} + e^{x} x^{3} + e^{2 x} x

Solution steps

(e^{x} + x e^{x}) (x^{2} + e^{x})

= (e^{x} + e^{x} x) (x^{2} + e^{x})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = e^{x}, b = x e^{x}, c = x^{2}, d = e^{x}

= e^{x} x^{2} + e^{x} e^{x} + x e^{x} x^{2} + x e^{x} e^{x}

= e^{x} x^{2} + e^{x} e^{x} + e^{x} x^{2} x + e^{x} e^{x} x

Simplify

e^{x} x^{2} + e^{x} e^{x} + e^{x} x^{2} x + e^{x} e^{x} x : e^{x} x^{2} + e^{2 x} + e^{x} x^{3} + e^{2 x} x

= e^{x} x^{2} + e^{2 x} + e^{x} x^{3} + e^{2 x} x

(x^{2} + 5 - 3) (x^{2} + 5 + 3)

lo g_{3} (x) (\frac{x ^{2}}{81 y ^{4}})

- \frac{6 ( sec ^{2} ( x ) + cos ( x ) )}{tan ( x ) + sin ( x )}

12 \times (\frac{x + 2}{6} - 5)

What is expand (e^x+xe^x)(x^2+e^x) ?
The solution to expand (e^x+xe^x)(x^2+e^x) is e^xx^2+e^{2x}+e^xx^3+e^{2x}x