Write in Standard Form (3x-4)(x^2-5x-1)

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

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Expand $(3 x - 4) (x^{2} - 5 x - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $- 5$ .

$3 x^{3} - 15 x^{2} + 3 x \cdot - 1 - 4 x^{2} - 4 (- 5 x) - 4 \cdot - 1$

Multiply $- 1$ by $3$ .

$3 x^{3} - 15 x^{2} - 3 x - 4 x^{2} - 4 (- 5 x) - 4 \cdot - 1$

Multiply $- 5$ by $- 4$ .

$3 x^{3} - 15 x^{2} - 3 x - 4 x^{2} + 20 x - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$3 x^{3} - 15 x^{2} - 3 x - 4 x^{2} + 20 x + 4$

Simplify by adding terms.

Subtract $4 x^{2}$ from $- 15 x^{2}$ .

$3 x^{3} - 19 x^{2} - 3 x + 20 x + 4$

Add $- 3 x$ and $20 x$ .

$3 x^{3} - 19 x^{2} + 17 x + 4$