Find the Product (17+e^2)(17-e^2)

$(17 + e^{2}) (17 - e^{2})$

Step 1

Expand $(17 + e^{2}) (17 - e^{2})$ using the FOIL Method.

Apply the distributive property.

$17 (17 - e^{2}) + e^{2} (17 - e^{2})$

Apply the distributive property.

$17 \cdot 17 + 17 (- e^{2}) + e^{2} (17 - e^{2})$

Apply the distributive property.

$17 \cdot 17 + 17 (- e^{2}) + e^{2} \cdot 17 + e^{2} (- e^{2})$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $17$ by $17$ .

$289 + 17 (- e^{2}) + e^{2} \cdot 17 + e^{2} (- e^{2})$

Multiply $- 1$ by $17$ .

$289 - 17 e^{2} + e^{2} \cdot 17 + e^{2} (- e^{2})$

Move $17$ to the left of $e^{2}$ .

$289 - 17 e^{2} + 17 \cdot e^{2} + e^{2} (- e^{2})$

Multiply $e^{2}$ by $e^{2}$ by adding the exponents.

Move $e^{2}$ .

$289 - 17 e^{2} + 17 e^{2} + e^{2} e^{2} \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$289 - 17 e^{2} + 17 e^{2} + e^{2 + 2} \cdot - 1$

Add $2$ and $2$ .

$289 - 17 e^{2} + 17 e^{2} + e^{4} \cdot - 1$

Move $- 1$ to the left of $e^{4}$ .

$289 - 17 e^{2} + 17 e^{2} - 1 \cdot e^{4}$

Rewrite $- 1 e^{4}$ as $- e^{4}$ .

$289 - 17 e^{2} + 17 e^{2} - e^{4}$

Add $- 17 e^{2}$ and $17 e^{2}$ .

$289 + 0 - e^{4}$

Add $289$ and $0$ .

$289 - e^{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$289 - e^{4}$

Decimal Form:

$234.40184996 \dots$