Simplify (m^2-5)(2m^2+3)

$(m^{2} - 5) (2 m^{2} + 3)$

Step 1

Expand $(m^{2} - 5) (2 m^{2} + 3)$ using the FOIL Method.

Apply the distributive property.

$m^{2} (2 m^{2} + 3) - 5 (2 m^{2} + 3)$

Apply the distributive property.

$m^{2} (2 m^{2}) + m^{2} \cdot 3 - 5 (2 m^{2} + 3)$

Apply the distributive property.

$m^{2} (2 m^{2}) + m^{2} \cdot 3 - 5 (2 m^{2}) - 5 \cdot 3$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 m^{2} m^{2} + m^{2} \cdot 3 - 5 (2 m^{2}) - 5 \cdot 3$

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

Move $m^{2}$ .

$2 (m^{2} m^{2}) + m^{2} \cdot 3 - 5 (2 m^{2}) - 5 \cdot 3$

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

$2 m^{2 + 2} + m^{2} \cdot 3 - 5 (2 m^{2}) - 5 \cdot 3$

Add $2$ and $2$ .

$2 m^{4} + m^{2} \cdot 3 - 5 (2 m^{2}) - 5 \cdot 3$

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

$2 m^{4} + 3 \cdot m^{2} - 5 (2 m^{2}) - 5 \cdot 3$

Multiply $2$ by $- 5$ .

$2 m^{4} + 3 m^{2} - 10 m^{2} - 5 \cdot 3$

Multiply $- 5$ by $3$ .

$2 m^{4} + 3 m^{2} - 10 m^{2} - 15$

Subtract $10 m^{2}$ from $3 m^{2}$ .

$2 m^{4} - 7 m^{2} - 15$