Write in Standard Form 3(x+1)(x+3)(x-4)

$3 (x + 1) (x + 3) (x - 4)$

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

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

Simplify by multiplying through.

Apply the distributive property.

$(3 x + 3 \cdot 1) (x + 3) (x - 4)$

Multiply $3$ by $1$ .

$(3 x + 3) (x + 3) (x - 4)$

Expand $(3 x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$(3 x (x + 3) + 3 (x + 3)) (x - 4)$

Apply the distributive property.

$(3 x \cdot x + 3 x \cdot 3 + 3 (x + 3)) (x - 4)$

Apply the distributive property.

$(3 x \cdot x + 3 x \cdot 3 + 3 x + 3 \cdot 3) (x - 4)$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$(3 (x \cdot x) + 3 x \cdot 3 + 3 x + 3 \cdot 3) (x - 4)$

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$(3 x^{2} + 9 x + 3 x + 3 \cdot 3) (x - 4)$

Multiply $3$ by $3$ .

$(3 x^{2} + 9 x + 3 x + 9) (x - 4)$

Add $9 x$ and $3 x$ .

$(3 x^{2} + 12 x + 9) (x - 4)$

Expand $(3 x^{2} + 12 x + 9) (x - 4)$ by multiplying each term in the first expression by each term in the second expression.

$3 x^{2} x + 3 x^{2} \cdot - 4 + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

Simplify terms.

Simplify each term.

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

Move $x$ .

$3 (x \cdot x^{2}) + 3 x^{2} \cdot - 4 + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

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

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

$3 (x^{1} x^{2}) + 3 x^{2} \cdot - 4 + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

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

$3 x^{1 + 2} + 3 x^{2} \cdot - 4 + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

Add $1$ and $2$ .

$3 x^{3} + 3 x^{2} \cdot - 4 + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

Multiply $- 4$ by $3$ .

$3 x^{3} - 12 x^{2} + 12 x \cdot x + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

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

Move $x$ .

$3 x^{3} - 12 x^{2} + 12 (x \cdot x) + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

Multiply $x$ by $x$ .

$3 x^{3} - 12 x^{2} + 12 x^{2} + 12 x \cdot - 4 + 9 x + 9 \cdot - 4$

Multiply $- 4$ by $12$ .

$3 x^{3} - 12 x^{2} + 12 x^{2} - 48 x + 9 x + 9 \cdot - 4$

Multiply $9$ by $- 4$ .

$3 x^{3} - 12 x^{2} + 12 x^{2} - 48 x + 9 x - 36$

Simplify by adding terms.

Combine the opposite terms in $3 x^{3} - 12 x^{2} + 12 x^{2} - 48 x + 9 x - 36$ .

Add $- 12 x^{2}$ and $12 x^{2}$ .

$3 x^{3} + 0 - 48 x + 9 x - 36$

Add $3 x^{3}$ and $0$ .

$3 x^{3} - 48 x + 9 x - 36$

Add $- 48 x$ and $9 x$ .

$3 x^{3} - 39 x - 36$

Write in Standard Form 3(x+1)(x+3)(x-4)

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