Simplify (b^2-1)(b^2+3)

$(b^{2} - 1) (b^{2} + 3)$

Step 1

Expand $(b^{2} - 1) (b^{2} + 3)$ using the FOIL Method.

Apply the distributive property.

$b^{2} (b^{2} + 3) - 1 (b^{2} + 3)$

Apply the distributive property.

$b^{2} b^{2} + b^{2} \cdot 3 - 1 (b^{2} + 3)$

Apply the distributive property.

$b^{2} b^{2} + b^{2} \cdot 3 - 1 b^{2} - 1 \cdot 3$

Step 2

Simplify and combine like terms.

Simplify each term.

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

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

$b^{2 + 2} + b^{2} \cdot 3 - 1 b^{2} - 1 \cdot 3$

Add $2$ and $2$ .

$b^{4} + b^{2} \cdot 3 - 1 b^{2} - 1 \cdot 3$

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

$b^{4} + 3 \cdot b^{2} - 1 b^{2} - 1 \cdot 3$

Rewrite $- 1 b^{2}$ as $- b^{2}$ .

$b^{4} + 3 b^{2} - b^{2} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

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

Subtract $b^{2}$ from $3 b^{2}$ .

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