Find the Product x^3(x^2+5x+1)

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

Apply the distributive property.

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

Simplify.

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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

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

Add $3$ and $2$ .

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

Rewrite using the commutative property of multiplication.

$x^{5} + 5 x^{3} x + x^{3} \cdot 1$

Multiply $x^{3}$ by $1$ .

$x^{5} + 5 x^{3} x + x^{3}$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$x^{5} + 5 (x \cdot x^{3}) + x^{3}$

Multiply $x$ by $x^{3}$ .

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

$x^{5} + 5 (x^{1} x^{3}) + x^{3}$

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

$x^{5} + 5 x^{1 + 3} + x^{3}$

Add $1$ and $3$ .

$x^{5} + 5 x^{4} + x^{3}$