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

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Multiply $4$ by $- 5$ .

$(4 x - 20) (x^{2} + x + 2)$

Step 2

Expand $(4 x - 20) (x^{2} + x + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

$4 (x^{2} x) + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

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

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

$4 (x^{2} x^{1}) + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

$4 x^{3} + 4 (x \cdot x) + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Multiply $x$ by $x$ .

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

Multiply $2$ by $4$ .

$4 x^{3} + 4 x^{2} + 8 x - 20 x^{2} - 20 x - 20 \cdot 2$

Multiply $- 20$ by $2$ .

$4 x^{3} + 4 x^{2} + 8 x - 20 x^{2} - 20 x - 40$

Simplify by adding terms.

Subtract $20 x^{2}$ from $4 x^{2}$ .

$4 x^{3} - 16 x^{2} + 8 x - 20 x - 40$

Subtract $20 x$ from $8 x$ .

$4 x^{3} - 16 x^{2} - 12 x - 40$