Simplify 13p-3p(1-2m)-m(2m-5p)-m^2

$13 p - 3 p (1 - 2 m) - m (2 m - 5 p) - m^{2}$

Step 1

Simplify each term.

Apply the distributive property.

$13 p - 3 p \cdot 1 - 3 p (- 2 m) - m (2 m - 5 p) - m^{2}$

Multiply $- 3$ by $1$ .

$13 p - 3 p - 3 p (- 2 m) - m (2 m - 5 p) - m^{2}$

Rewrite using the commutative property of multiplication.

$13 p - 3 p - 3 \cdot - 2 p m - m (2 m - 5 p) - m^{2}$

Multiply $- 3$ by $- 2$ .

$13 p - 3 p + 6 p m - m (2 m - 5 p) - m^{2}$

Apply the distributive property.

$13 p - 3 p + 6 p m - m (2 m) - m (- 5 p) - m^{2}$

Rewrite using the commutative property of multiplication.

$13 p - 3 p + 6 p m - 1 \cdot 2 m \cdot m - m (- 5 p) - m^{2}$

Rewrite using the commutative property of multiplication.

$13 p - 3 p + 6 p m - 1 \cdot 2 m \cdot m - 1 \cdot - 5 m p - m^{2}$

Simplify each term.

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

Move $m$ .

$13 p - 3 p + 6 p m - 1 \cdot 2 (m \cdot m) - 1 \cdot - 5 m p - m^{2}$

Multiply $m$ by $m$ .

$13 p - 3 p + 6 p m - 1 \cdot 2 m^{2} - 1 \cdot - 5 m p - m^{2}$

Multiply $- 1$ by $2$ .

$13 p - 3 p + 6 p m - 2 m^{2} - 1 \cdot - 5 m p - m^{2}$

Multiply $- 1$ by $- 5$ .

$13 p - 3 p + 6 p m - 2 m^{2} + 5 m p - m^{2}$

Step 2

Subtract $3 p$ from $13 p$ .

$10 p + 6 p m - 2 m^{2} + 5 m p - m^{2}$

Step 3

Add $6 p m$ and $5 m p$ .

Move $p$ .

$10 p - 2 m^{2} + 6 m p + 5 m p - m^{2}$

Add $6 m p$ and $5 m p$ .

$10 p - 2 m^{2} + 11 m p - m^{2}$

Step 4

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

$10 p - 3 m^{2} + 11 m p$

Step 5

Simplify the expression.

Move $10 p$ .

$- 3 m^{2} + 11 m p + 10 p$

Reorder $- 3 m^{2}$ and $11 m p$ .

$11 m p - 3 m^{2} + 10 p$