Simplify (x+2)(2x-3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $- 3$ to the left of $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 3$ .

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

Add $- 3 x$ and $4 x$ .

$2 x^{2} + x - 6$