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

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

Simplify each term.

Expand $(2 m - 5) (2 m - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

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

Multiply $m$ by $m$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 3$ by $2$ .

$4 m^{2} - 6 m - 5 (2 m) - 5 \cdot - 3 - (m^{2} + 5 m)$

Multiply $2$ by $- 5$ .

$4 m^{2} - 6 m - 10 m - 5 \cdot - 3 - (m^{2} + 5 m)$

Multiply $- 5$ by $- 3$ .

$4 m^{2} - 6 m - 10 m + 15 - (m^{2} + 5 m)$

Subtract $10 m$ from $- 6 m$ .

$4 m^{2} - 16 m + 15 - (m^{2} + 5 m)$

Apply the distributive property.

$4 m^{2} - 16 m + 15 - m^{2} - (5 m)$

Multiply $5$ by $- 1$ .

$4 m^{2} - 16 m + 15 - m^{2} - 5 m$

Simplify by adding terms.

Subtract $m^{2}$ from $4 m^{2}$ .

$3 m^{2} - 16 m + 15 - 5 m$

Subtract $5 m$ from $- 16 m$ .

$3 m^{2} - 21 m + 15$