Simplify 4(a^2-7a(-4a-3(a^2-2a)))

$4 (a^{2} - 7 a (- 4 a - 3 (a^{2} - 2 a)))$

Simplify each term.

Apply the distributive property.

$4 (a^{2} - 7 a (- 4 a - 3 a^{2} - 3 (- 2 a)))$

Multiply $- 2$ by $- 3$ .

$4 (a^{2} - 7 a (- 4 a - 3 a^{2} + 6 a))$

Add $- 4 a$ and $6 a$ .

$4 (a^{2} - 7 a (- 3 a^{2} + 2 a))$

Apply the distributive property.

$4 (a^{2} - 7 a (- 3 a^{2}) - 7 a (2 a))$

Rewrite using the commutative property of multiplication.

$4 (a^{2} - 7 \cdot - 3 a \cdot a^{2} - 7 a (2 a))$

Rewrite using the commutative property of multiplication.

$4 (a^{2} - 7 \cdot - 3 a \cdot a^{2} - 7 \cdot 2 a \cdot a)$

Simplify each term.

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

Move $a^{2}$ .

$4 (a^{2} - 7 \cdot - 3 (a^{2} a) - 7 \cdot 2 a \cdot a)$

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

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

$4 (a^{2} - 7 \cdot - 3 (a^{2} a^{1}) - 7 \cdot 2 a \cdot a)$

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

$4 (a^{2} - 7 \cdot - 3 a^{2 + 1} - 7 \cdot 2 a \cdot a)$

Add $2$ and $1$ .

$4 (a^{2} - 7 \cdot - 3 a^{3} - 7 \cdot 2 a \cdot a)$

Multiply $- 7$ by $- 3$ .

$4 (a^{2} + 21 a^{3} - 7 \cdot 2 a \cdot a)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$4 (a^{2} + 21 a^{3} - 7 \cdot 2 (a \cdot a))$

Multiply $a$ by $a$ .

$4 (a^{2} + 21 a^{3} - 7 \cdot 2 a^{2})$

Multiply $- 7$ by $2$ .

$4 (a^{2} + 21 a^{3} - 14 a^{2})$

Simplify terms.

Subtract $14 a^{2}$ from $a^{2}$ .

$4 (21 a^{3} - 13 a^{2})$

Apply the distributive property.

$4 (21 a^{3}) + 4 (- 13 a^{2})$

Multiply.

Multiply $21$ by $4$ .

$84 a^{3} + 4 (- 13 a^{2})$

Multiply $- 13$ by $4$ .

$84 a^{3} - 52 a^{2}$