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

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

Step 1

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

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

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x + x^{2} \cdot - 4 + x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4$ .

Reorder the factors in the terms $x \cdot - 4$ and $4 x$ .

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

Add $- 4 x$ and $4 x$ .

$x^{2} x + x^{2} \cdot - 4 + x \cdot x + 0 + 4 \cdot - 4$

Add $x^{2} x + x^{2} \cdot - 4 + x \cdot x$ and $0$ .

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

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $- 4$ .

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

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

$x^{3} - 3 x^{2} - 16$