Simplify (x-4)(3x^2+x-5)

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

Expand $(x - 4) (3 x^{2} + x - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $x$ by $x$ .

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

Move $- 5$ to the left of $x$ .

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

Multiply $3$ by $- 4$ .

$3 x^{3} + x^{2} - 5 x - 12 x^{2} - 4 x - 4 \cdot - 5$

Multiply $- 4$ by $- 5$ .

$3 x^{3} + x^{2} - 5 x - 12 x^{2} - 4 x + 20$

Simplify by adding terms.

Subtract $12 x^{2}$ from $x^{2}$ .

$3 x^{3} - 11 x^{2} - 5 x - 4 x + 20$

Subtract $4 x$ from $- 5 x$ .

$3 x^{3} - 11 x^{2} - 9 x + 20$