calc((1+e)^2) — step-by-step solution

Let's calculate:

{(1 + e)}^{2}

ⓘ Raising a sum to a positive integer power means multiplying it by itself as many times as the exponent indicates:

{(1 + e)}^{2}

(1 + e) \times (1 + e)

(1 + e) \times (1 + e)

ⓘ Expand using the distributive law, multiplying each term of the sum by the other factor:

(1 + e) \times (1 + e)

1 \times 1

+ 1 \times e

+ e \times 1

+ e \times e

1 \times 1

+ 1 \times e

+ e \times 1

+ e \times e

ⓘ Perform multiplications before additions and subtractions:

1 \times 1

1

■Multiplying powers with the same base adds the exponents:

e \times e

e^{2}

1

+ e

+ e

+ e^{2}

ⓘ Like terms are grouped by adding their coefficients:

e + e

2 e

1 + 2 e + e^{2}

▶Result:

e^{2} + 2 e + 1

The numeric value of:

e^{2} + 2 e + 1

is:

{\approx 2.7183}^{2} + 2 \times \approx 2.7183 + 1

\approx 7.3891 + \approx 5.4366 + 1

\approx 12.8256 + 1

▷

\approx 13.8256