Simplify (4x-2)*(6(2x+7))

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Multiply.

Multiply $2$ by $6$ .

$(4 x - 2) \cdot (12 x + 6 \cdot 7)$

Multiply $6$ by $7$ .

$(4 x - 2) \cdot (12 x + 42)$

Step 2

Expand $(4 x - 2) (12 x + 42)$ using the FOIL Method.

Apply the distributive property.

$4 x (12 x + 42) - 2 (12 x + 42)$

Apply the distributive property.

$4 x (12 x) + 4 x \cdot 42 - 2 (12 x + 42)$

Apply the distributive property.

$4 x (12 x) + 4 x \cdot 42 - 2 (12 x) - 2 \cdot 42$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 12 x \cdot x + 4 x \cdot 42 - 2 (12 x) - 2 \cdot 42$

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

Move $x$ .

$4 \cdot 12 (x \cdot x) + 4 x \cdot 42 - 2 (12 x) - 2 \cdot 42$

Multiply $x$ by $x$ .

$4 \cdot 12 x^{2} + 4 x \cdot 42 - 2 (12 x) - 2 \cdot 42$

Multiply $4$ by $12$ .

$48 x^{2} + 4 x \cdot 42 - 2 (12 x) - 2 \cdot 42$

Multiply $42$ by $4$ .

$48 x^{2} + 168 x - 2 (12 x) - 2 \cdot 42$

Multiply $12$ by $- 2$ .

$48 x^{2} + 168 x - 24 x - 2 \cdot 42$

Multiply $- 2$ by $42$ .

$48 x^{2} + 168 x - 24 x - 84$

Subtract $24 x$ from $168 x$ .

$48 x^{2} + 144 x - 84$