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

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

Simplify each term.

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Apply the distributive property.

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

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

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Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 4$ by $- 2$ .

$- 2 a^{3} + 8 a + a (a^{2} - 3)$

Apply the distributive property.

$- 2 a^{3} + 8 a + a \cdot a^{2} + a \cdot - 3$

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

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

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

$- 2 a^{3} + 8 a + a^{1} a^{2} + a \cdot - 3$

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

$- 2 a^{3} + 8 a + a^{1 + 2} + a \cdot - 3$

Add $1$ and $2$ .

$- 2 a^{3} + 8 a + a^{3} + a \cdot - 3$

Move $- 3$ to the left of $a$ .

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

Simplify by adding terms.

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Add $- 2 a^{3}$ and $a^{3}$ .

$- a^{3} + 8 a - 3 a$

Subtract $3 a$ from $8 a$ .

$- a^{3} + 5 a$

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