Write in Standard Form (4b^2+3)(4b^2-3)

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

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 $(4 b^{2} + 3) (4 b^{2} - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify terms.

Combine the opposite terms in $4 b^{2} (4 b^{2}) + 4 b^{2} \cdot - 3 + 3 (4 b^{2}) + 3 \cdot - 3$ .

Reorder the factors in the terms $4 b^{2} \cdot - 3$ and $3 (4 b^{2})$ .

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

Add $- 3 \cdot 4 b^{2}$ and $3 \cdot 4 b^{2}$ .

$4 b^{2} (4 b^{2}) + 0 + 3 \cdot - 3$

Add $4 b^{2} (4 b^{2})$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $b^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $4$ by $4$ .

$16 b^{4} + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$16 b^{4} - 9$