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

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

Step 1

Expand $(4 - x) (x^{2} - 3 x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $4$ .

$4 x^{2} - 12 x - x \cdot x^{2} - x (- 3 x)$

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

Move $x^{2}$ .

$4 x^{2} - 12 x - (x^{2} x) - x (- 3 x)$

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

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

$4 x^{2} - 12 x - (x^{2} x^{1}) - x (- 3 x)$

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

$4 x^{2} - 12 x - x^{2 + 1} - x (- 3 x)$

Add $2$ and $1$ .

$4 x^{2} - 12 x - x^{3} - x (- 3 x)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 12 x - x^{3} - 1 \cdot - 3 x \cdot x$

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

Move $x$ .

$4 x^{2} - 12 x - x^{3} - 1 \cdot - 3 (x \cdot x)$

Multiply $x$ by $x$ .

$4 x^{2} - 12 x - x^{3} - 1 \cdot - 3 x^{2}$

Multiply $- 1$ by $- 3$ .

$4 x^{2} - 12 x - x^{3} + 3 x^{2}$

Add $4 x^{2}$ and $3 x^{2}$ .

$7 x^{2} - 12 x - x^{3}$

Step 3

Move $- 12 x$ .

$7 x^{2} - x^{3} - 12 x$

Step 4

Reorder $7 x^{2}$ and $- x^{3}$ .

$- x^{3} + 7 x^{2} - 12 x$