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

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

Step 1

Expand $(x + 3) (x + 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $3$ by $1$ .

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

Add $x$ and $3 x$ .

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

Step 3

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

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

Step 4

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 4$ to the left of $x^{2}$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 4$ by $4$ .

$x^{3} - 4 x^{2} + 4 x^{2} - 16 x + 3 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$x^{3} - 4 x^{2} + 4 x^{2} - 16 x + 3 x - 12$

Simplify by adding terms.

Combine the opposite terms in $x^{3} - 4 x^{2} + 4 x^{2} - 16 x + 3 x - 12$ .

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

$x^{3} + 0 - 16 x + 3 x - 12$

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

$x^{3} - 16 x + 3 x - 12$

Add $- 16 x$ and $3 x$ .

$x^{3} - 13 x - 12$

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

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