Simplify (7x^2-6x-6)(2x-4)

$(7 x^{2} - 6 x - 6) (2 x - 4)$

Step 1

Expand $(7 x^{2} - 6 x - 6) (2 x - 4)$ by multiplying each term in the first expression by each term in the second expression.

$7 x^{2} (2 x) + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 2 x^{2} x + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

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

Move $x$ .

$7 \cdot 2 (x \cdot x^{2}) + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

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

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

$7 \cdot 2 (x^{1} x^{2}) + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

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

$7 \cdot 2 x^{1 + 2} + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Add $1$ and $2$ .

$7 \cdot 2 x^{3} + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $7$ by $2$ .

$14 x^{3} + 7 x^{2} \cdot - 4 - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $- 4$ by $7$ .

$14 x^{3} - 28 x^{2} - 6 x (2 x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Rewrite using the commutative property of multiplication.

$14 x^{3} - 28 x^{2} - 6 \cdot 2 x \cdot x - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$14 x^{3} - 28 x^{2} - 6 \cdot 2 (x \cdot x) - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $x$ by $x$ .

$14 x^{3} - 28 x^{2} - 6 \cdot 2 x^{2} - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $- 6$ by $2$ .

$14 x^{3} - 28 x^{2} - 12 x^{2} - 6 x \cdot - 4 - 6 (2 x) - 6 \cdot - 4$

Multiply $- 4$ by $- 6$ .

$14 x^{3} - 28 x^{2} - 12 x^{2} + 24 x - 6 (2 x) - 6 \cdot - 4$

Multiply $2$ by $- 6$ .

$14 x^{3} - 28 x^{2} - 12 x^{2} + 24 x - 12 x - 6 \cdot - 4$

Multiply $- 6$ by $- 4$ .

$14 x^{3} - 28 x^{2} - 12 x^{2} + 24 x - 12 x + 24$

Simplify by adding terms.

Subtract $12 x^{2}$ from $- 28 x^{2}$ .

$14 x^{3} - 40 x^{2} + 24 x - 12 x + 24$

Subtract $12 x$ from $24 x$ .

$14 x^{3} - 40 x^{2} + 12 x + 24$