Simplify 4x(2x^2-7x+3)

$4 x (2 x^{2} - 7 x + 3)$

Step 1

Apply the distributive property.

$4 x (2 x^{2}) + 4 x (- 7 x) + 4 x \cdot 3$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x \cdot x^{2} + 4 x (- 7 x) + 4 x \cdot 3$

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x \cdot x^{2} + 4 \cdot - 7 x \cdot x + 4 x \cdot 3$

Multiply $3$ by $4$ .

$4 \cdot 2 x \cdot x^{2} + 4 \cdot - 7 x \cdot x + 12 x$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$4 \cdot 2 (x^{2} x) + 4 \cdot - 7 x \cdot x + 12 x$

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

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

$4 \cdot 2 (x^{2} x^{1}) + 4 \cdot - 7 x \cdot x + 12 x$

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

$4 \cdot 2 x^{2 + 1} + 4 \cdot - 7 x \cdot x + 12 x$

Add $2$ and $1$ .

$4 \cdot 2 x^{3} + 4 \cdot - 7 x \cdot x + 12 x$

Multiply $4$ by $2$ .

$8 x^{3} + 4 \cdot - 7 x \cdot x + 12 x$

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

Move $x$ .

$8 x^{3} + 4 \cdot - 7 (x \cdot x) + 12 x$

Multiply $x$ by $x$ .

$8 x^{3} + 4 \cdot - 7 x^{2} + 12 x$

Multiply $4$ by $- 7$ .

$8 x^{3} - 28 x^{2} + 12 x$