Simplify 4b^2(b^3-8)

$4 b^{2} (b^{3} - 8)$

Apply the distributive property.

$4 b^{2} b^{3} + 4 b^{2} \cdot - 8$

Multiply $b^{2}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$4 (b^{3} b^{2}) + 4 b^{2} \cdot - 8$

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

$4 b^{3 + 2} + 4 b^{2} \cdot - 8$

Add $3$ and $2$ .

$4 b^{5} + 4 b^{2} \cdot - 8$

Multiply $- 8$ by $4$ .

$4 b^{5} - 32 b^{2}$