Write in Standard Form (3+b^2)(3-b^2)

$(3 + b^{2}) (3 - b^{2})$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(3 + b^{2}) (3 - b^{2})$ using the FOIL Method.

Apply the distributive property.

$3 (3 - b^{2}) + b^{2} (3 - b^{2})$

Apply the distributive property.

$3 \cdot 3 + 3 (- b^{2}) + b^{2} (3 - b^{2})$

Apply the distributive property.

$3 \cdot 3 + 3 (- b^{2}) + b^{2} \cdot 3 + b^{2} (- b^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- b^{2}) + b^{2} \cdot 3 + b^{2} (- b^{2})$

Multiply $- 1$ by $3$ .

$9 - 3 b^{2} + b^{2} \cdot 3 + b^{2} (- b^{2})$

Move $3$ to the left of $b^{2}$ .

$9 - 3 b^{2} + 3 \cdot b^{2} + b^{2} (- b^{2})$

Rewrite using the commutative property of multiplication.

$9 - 3 b^{2} + 3 b^{2} - b^{2} b^{2}$

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

Move $b^{2}$ .

$9 - 3 b^{2} + 3 b^{2} - (b^{2} b^{2})$

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

$9 - 3 b^{2} + 3 b^{2} - b^{2 + 2}$

Add $2$ and $2$ .

$9 - 3 b^{2} + 3 b^{2} - b^{4}$

Add $- 3 b^{2}$ and $3 b^{2}$ .

$9 + 0 - b^{4}$

Add $9$ and $0$ .

$9 - b^{4}$

Step 4

Reorder $9$ and $- b^{4}$ .

$- b^{4} + 9$