Simplify x(2x+1)(x-3)

$x (2 x + 1) (x - 3)$

Apply the distributive property.

$(x (2 x) + x \cdot 1) (x - 3)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$(2 x \cdot x + x \cdot 1) (x - 3)$

Multiply $x$ by $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

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

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

$2 (x^{1} x^{2}) + 2 x^{2} \cdot - 3 + x \cdot x + x \cdot - 3$

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

$2 x^{1 + 2} + 2 x^{2} \cdot - 3 + x \cdot x + x \cdot - 3$

Add $1$ and $2$ .

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

Multiply $- 3$ by $2$ .

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

Multiply $x$ by $x$ .

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

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

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

Add $- 6 x^{2}$ and $x^{2}$ .

$2 x^{3} - 5 x^{2} - 3 x$