Simplify 4b(4ab^2+a-1)

$4 b (4 a b^{2} + a - 1)$

Step 1

Apply the distributive property.

$4 b (4 a b^{2}) + 4 b a + 4 b \cdot - 1$

Step 2

Simplify.

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

Move $b^{2}$ .

$4 (b^{2} b) (4 a) + 4 b a + 4 b \cdot - 1$

Multiply $b^{2}$ by $b$ .

Raise $b$ to the power of $1$ .

$4 (b^{2} b^{1}) (4 a) + 4 b a + 4 b \cdot - 1$

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

$4 b^{2 + 1} (4 a) + 4 b a + 4 b \cdot - 1$

Add $2$ and $1$ .

$4 b^{3} (4 a) + 4 b a + 4 b \cdot - 1$

Multiply $- 1$ by $4$ .

$4 b^{3} (4 a) + 4 b a - 4 b$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 b^{3} a + 4 b a - 4 b$

Multiply $4$ by $4$ .

$16 b^{3} a + 4 b a - 4 b$

Step 4

Reorder.

Move $b^{3}$ .

$16 a b^{3} + 4 b a - 4 b$

Move $b$ .

$16 a b^{3} + 4 a b - 4 b$