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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $3$ .

$3 a^{3} + 3 \cdot - 3 a \cdot a + 12 a - 4 (3 a^{3} - 2 a^{2})$

Simplify each term.

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

Move $a$ .

$3 a^{3} + 3 \cdot - 3 (a \cdot a) + 12 a - 4 (3 a^{3} - 2 a^{2})$

Multiply $a$ by $a$ .

$3 a^{3} + 3 \cdot - 3 a^{2} + 12 a - 4 (3 a^{3} - 2 a^{2})$

Multiply $3$ by $- 3$ .

$3 a^{3} - 9 a^{2} + 12 a - 4 (3 a^{3} - 2 a^{2})$

Apply the distributive property.

$3 a^{3} - 9 a^{2} + 12 a - 4 (3 a^{3}) - 4 (- 2 a^{2})$

Multiply $3$ by $- 4$ .

$3 a^{3} - 9 a^{2} + 12 a - 12 a^{3} - 4 (- 2 a^{2})$

Multiply $- 2$ by $- 4$ .

$3 a^{3} - 9 a^{2} + 12 a - 12 a^{3} + 8 a^{2}$

Step 2

Simplify by adding terms.

Subtract $12 a^{3}$ from $3 a^{3}$ .

$- 9 a^{3} - 9 a^{2} + 12 a + 8 a^{2}$

Add $- 9 a^{2}$ and $8 a^{2}$ .

$- 9 a^{3} - a^{2} + 12 a$