Find the Product 3x(5x^2-x+4)

$3 x (5 x^{2} - x + 4)$

Apply the distributive property.

$3 x (5 x^{2}) + 3 x (- x) + 3 x \cdot 4$

Simplify.

Rewrite using the commutative property of multiplication.

$3 \cdot 5 x \cdot x^{2} + 3 x (- x) + 3 x \cdot 4$

Rewrite using the commutative property of multiplication.

$3 \cdot 5 x \cdot x^{2} + 3 \cdot - 1 x \cdot x + 3 x \cdot 4$

Multiply $4$ by $3$ .

$3 \cdot 5 x \cdot x^{2} + 3 \cdot - 1 x \cdot x + 12 x$

Simplify each term.

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

Move $x^{2}$ .

$3 \cdot 5 (x^{2} x) + 3 \cdot - 1 x \cdot x + 12 x$

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

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

$3 \cdot 5 (x^{2} x^{1}) + 3 \cdot - 1 x \cdot x + 12 x$

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

$3 \cdot 5 x^{2 + 1} + 3 \cdot - 1 x \cdot x + 12 x$

Add $2$ and $1$ .

$3 \cdot 5 x^{3} + 3 \cdot - 1 x \cdot x + 12 x$

Multiply $3$ by $5$ .

$15 x^{3} + 3 \cdot - 1 x \cdot x + 12 x$

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

Move $x$ .

$15 x^{3} + 3 \cdot - 1 (x \cdot x) + 12 x$

Multiply $x$ by $x$ .

$15 x^{3} + 3 \cdot - 1 x^{2} + 12 x$

Multiply $3$ by $- 1$ .

$15 x^{3} - 3 x^{2} + 12 x$