Simplify (a^2+a-4)*(2a^2-a-1)

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

Expand $(a^{2} + a - 4) (2 a^{2} - a - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $- 1$ to the left of $a^{2}$ .

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

Rewrite $- 1 a^{2}$ as $- a^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Move $- 1$ to the left of $a$ .

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

Rewrite $- 1 a$ as $- a$ .

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

Multiply $2$ by $- 4$ .

$2 a^{4} - a^{3} - a^{2} + 2 a^{3} - a^{2} - a - 8 a^{2} - 4 (- a) - 4 \cdot - 1$

Multiply $- 1$ by $- 4$ .

$2 a^{4} - a^{3} - a^{2} + 2 a^{3} - a^{2} - a - 8 a^{2} + 4 a - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$2 a^{4} - a^{3} - a^{2} + 2 a^{3} - a^{2} - a - 8 a^{2} + 4 a + 4$

Simplify by adding terms.

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

$2 a^{4} + a^{3} - a^{2} - a^{2} - a - 8 a^{2} + 4 a + 4$

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

$2 a^{4} + a^{3} - 2 a^{2} - a - 8 a^{2} + 4 a + 4$

Subtract $8 a^{2}$ from $- 2 a^{2}$ .

$2 a^{4} + a^{3} - 10 a^{2} - a + 4 a + 4$

Add $- a$ and $4 a$ .

$2 a^{4} + a^{3} - 10 a^{2} + 3 a + 4$

Simplify (a^2+a-4)*(2a^2-a-1)

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