What is expand (1+e*t)^2 ?

The solution to expand (1+e*t)^2 is e^2t^2+2et+1

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expand (1+e*t)^2

expand

(1 + e \cdot t)^{2}

e^{2} t^{2} + 2 e t + 1

Solution steps

(1 + e t)^{2}

Apply Perfect Square Formula:

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

a = 1, b = e t

= 1^{2} + 2 \cdot 1 e t + (e t)^{2}

Simplify

1^{2} + 2 \cdot 1 e t + (e t)^{2} : 1 + 2 e t + e^{2} t^{2}

= 1 + 2 e t + e^{2} t^{2}

Rewrite in standard form

= e^{2} t^{2} + 2 e t + 1

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