Simplify 4b(-5b-3)-2(b^2-7b-4)

$4 b (- 5 b - 3) - 2 (b^{2} - 7 b - 4)$

Simplify each term.

Apply the distributive property.

$4 b (- 5 b) + 4 b \cdot - 3 - 2 (b^{2} - 7 b - 4)$

Rewrite using the commutative property of multiplication.

$4 \cdot - 5 b \cdot b + 4 b \cdot - 3 - 2 (b^{2} - 7 b - 4)$

Multiply $- 3$ by $4$ .

$4 \cdot - 5 b \cdot b - 12 b - 2 (b^{2} - 7 b - 4)$

Simplify each term.

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$4 \cdot - 5 (b \cdot b) - 12 b - 2 (b^{2} - 7 b - 4)$

Multiply $b$ by $b$ .

$4 \cdot - 5 b^{2} - 12 b - 2 (b^{2} - 7 b - 4)$

Multiply $4$ by $- 5$ .

$- 20 b^{2} - 12 b - 2 (b^{2} - 7 b - 4)$

Apply the distributive property.

$- 20 b^{2} - 12 b - 2 b^{2} - 2 (- 7 b) - 2 \cdot - 4$

Simplify.

Multiply $- 7$ by $- 2$ .

$- 20 b^{2} - 12 b - 2 b^{2} + 14 b - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$- 20 b^{2} - 12 b - 2 b^{2} + 14 b + 8$

Simplify by adding terms.

Subtract $2 b^{2}$ from $- 20 b^{2}$ .

$- 22 b^{2} - 12 b + 14 b + 8$

Add $- 12 b$ and $14 b$ .

$- 22 b^{2} + 2 b + 8$