Find the Product 2x(3-x+5x^2)

$2 x (3 - x + 5 x^{2})$

Apply the distributive property.

$2 x \cdot 3 + 2 x (- x) + 2 x (5 x^{2})$

Simplify.

Multiply $3$ by $2$ .

$6 x + 2 x (- x) + 2 x (5 x^{2})$

Rewrite using the commutative property of multiplication.

$6 x + 2 \cdot - 1 x \cdot x + 2 x (5 x^{2})$

Rewrite using the commutative property of multiplication.

$6 x + 2 \cdot - 1 x \cdot x + 2 \cdot 5 x \cdot x^{2}$

Simplify each term.

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

Move $x$ .

$6 x + 2 \cdot - 1 (x \cdot x) + 2 \cdot 5 x \cdot x^{2}$

Multiply $x$ by $x$ .

$6 x + 2 \cdot - 1 x^{2} + 2 \cdot 5 x \cdot x^{2}$

Multiply $2$ by $- 1$ .

$6 x - 2 x^{2} + 2 \cdot 5 x \cdot x^{2}$

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

Move $x^{2}$ .

$6 x - 2 x^{2} + 2 \cdot 5 (x^{2} x)$

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

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

$6 x - 2 x^{2} + 2 \cdot 5 (x^{2} x^{1})$

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

$6 x - 2 x^{2} + 2 \cdot 5 x^{2 + 1}$

Add $2$ and $1$ .

$6 x - 2 x^{2} + 2 \cdot 5 x^{3}$

Multiply $2$ by $5$ .

$6 x - 2 x^{2} + 10 x^{3}$