What is expand (2e^{x^2}+x^2)^3 ?

The solution to expand (2e^{x^2}+x^2)^3 is 8e^{3x^2}+12e^{2x^2}x^2+6e^{x^2}x^4+x^6

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expand (2e^{x^2}+x^2)^3

expand

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

8 e^{3 x^{2}} + 12 e^{2 x^{2}} x^{2} + 6 e^{x^{2}} x^{4} + x^{6}

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(2 e^{x^{2}})^{3} + 3 (2 e^{x^{2}})^{2} x^{2} + 3 \cdot 2 e^{x^{2}} (x^{2})^{2} + (x^{2})^{3} : 8 e^{3 x^{2}} + 12 e^{2 x^{2}} x^{2} + 6 e^{x^{2}} x^{4} + x^{6}

= 8 e^{3 x^{2}} + 12 e^{2 x^{2}} x^{2} + 6 e^{x^{2}} x^{4} + x^{6}

(1 + x + x^{2})^{8}

3 (3 - 2)

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

\frac{d ^{2}}{d k ^{2}} ((y (k, x)) (e^{4 x} - k x))

x^{2} (1 - 4 e^{x})

What is expand (2e^{x^2}+x^2)^3 ?
The solution to expand (2e^{x^2}+x^2)^3 is 8e^{3x^2}+12e^{2x^2}x^2+6e^{x^2}x^4+x^6