Simplify (2a-9)(3a^2+4a-4)

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

Step 1

Expand $(2 a - 9) (3 a^{2} + 4 a - 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

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

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

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

$2 \cdot 3 (a^{2} a^{1}) + 2 a (4 a) + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

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

$2 \cdot 3 a^{2 + 1} + 2 a (4 a) + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Add $2$ and $1$ .

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

Multiply $2$ by $3$ .

$6 a^{3} + 2 a (4 a) + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Rewrite using the commutative property of multiplication.

$6 a^{3} + 2 \cdot 4 a \cdot a + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

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

Move $a$ .

$6 a^{3} + 2 \cdot 4 (a \cdot a) + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Multiply $a$ by $a$ .

$6 a^{3} + 2 \cdot 4 a^{2} + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Multiply $2$ by $4$ .

$6 a^{3} + 8 a^{2} + 2 a \cdot - 4 - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Multiply $- 4$ by $2$ .

$6 a^{3} + 8 a^{2} - 8 a - 9 (3 a^{2}) - 9 (4 a) - 9 \cdot - 4$

Multiply $3$ by $- 9$ .

$6 a^{3} + 8 a^{2} - 8 a - 27 a^{2} - 9 (4 a) - 9 \cdot - 4$

Multiply $4$ by $- 9$ .

$6 a^{3} + 8 a^{2} - 8 a - 27 a^{2} - 36 a - 9 \cdot - 4$

Multiply $- 9$ by $- 4$ .

$6 a^{3} + 8 a^{2} - 8 a - 27 a^{2} - 36 a + 36$

Simplify by adding terms.

Subtract $27 a^{2}$ from $8 a^{2}$ .

$6 a^{3} - 19 a^{2} - 8 a - 36 a + 36$

Subtract $36 a$ from $- 8 a$ .

$6 a^{3} - 19 a^{2} - 44 a + 36$