Simplify 5(x-3)(x^2+4x+1)

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Multiply $5$ by $- 3$ .

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

Step 2

Expand $(5 x - 15) (x^{2} + 4 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $4$ .

$5 x^{3} + 20 x^{2} + 5 x \cdot 1 - 15 x^{2} - 15 (4 x) - 15 \cdot 1$

Multiply $5$ by $1$ .

$5 x^{3} + 20 x^{2} + 5 x - 15 x^{2} - 15 (4 x) - 15 \cdot 1$

Multiply $4$ by $- 15$ .

$5 x^{3} + 20 x^{2} + 5 x - 15 x^{2} - 60 x - 15 \cdot 1$

Multiply $- 15$ by $1$ .

$5 x^{3} + 20 x^{2} + 5 x - 15 x^{2} - 60 x - 15$

Simplify by adding terms.

Subtract $15 x^{2}$ from $20 x^{2}$ .

$5 x^{3} + 5 x^{2} + 5 x - 60 x - 15$

Subtract $60 x$ from $5 x$ .

$5 x^{3} + 5 x^{2} - 55 x - 15$