Expand the Trigonometric Expression (x-2)(3x+4)

$(x - 2) (3 x + 4)$

Step 1

Expand $(x - 2) (3 x + 4)$ using the FOIL Method.

Apply the distributive property.

$x (3 x + 4) - 2 (3 x + 4)$

Apply the distributive property.

$x (3 x) + x \cdot 4 - 2 (3 x + 4)$

Apply the distributive property.

$x (3 x) + x \cdot 4 - 2 (3 x) - 2 \cdot 4$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 x \cdot x + x \cdot 4 - 2 (3 x) - 2 \cdot 4$

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

Move $x$ .

$3 (x \cdot x) + x \cdot 4 - 2 (3 x) - 2 \cdot 4$

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $4$ .

$3 x^{2} + 4 x - 6 x - 8$

Subtract $6 x$ from $4 x$ .

$3 x^{2} - 2 x - 8$