Simplify (4m^2-5)(4m^2+5)

$(4 m^{2} - 5) (4 m^{2} + 5)$

Step 1

Expand $(4 m^{2} - 5) (4 m^{2} + 5)$ using the FOIL Method.

Apply the distributive property.

$4 m^{2} (4 m^{2} + 5) - 5 (4 m^{2} + 5)$

Apply the distributive property.

$4 m^{2} (4 m^{2}) + 4 m^{2} \cdot 5 - 5 (4 m^{2} + 5)$

Apply the distributive property.

$4 m^{2} (4 m^{2}) + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 m^{2} m^{2} + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

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

Move $m^{2}$ .

$4 \cdot 4 (m^{2} m^{2}) + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

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

$4 \cdot 4 m^{2 + 2} + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

Add $2$ and $2$ .

$4 \cdot 4 m^{4} + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

Multiply $4$ by $4$ .

$16 m^{4} + 4 m^{2} \cdot 5 - 5 (4 m^{2}) - 5 \cdot 5$

Multiply $5$ by $4$ .

$16 m^{4} + 20 m^{2} - 5 (4 m^{2}) - 5 \cdot 5$

Multiply $4$ by $- 5$ .

$16 m^{4} + 20 m^{2} - 20 m^{2} - 5 \cdot 5$

Multiply $- 5$ by $5$ .

$16 m^{4} + 20 m^{2} - 20 m^{2} - 25$

Subtract $20 m^{2}$ from $20 m^{2}$ .

$16 m^{4} + 0 - 25$

Add $16 m^{4}$ and $0$ .

$16 m^{4} - 25$