Find the Product 7x^3(5x^2+3x+1)

$7 x^{3} (5 x^{2} + 3 x + 1)$

Apply the distributive property.

$7 x^{3} (5 x^{2}) + 7 x^{3} (3 x) + 7 x^{3} \cdot 1$

Simplify.

Rewrite using the commutative property of multiplication.

$7 \cdot 5 x^{3} x^{2} + 7 x^{3} (3 x) + 7 x^{3} \cdot 1$

Rewrite using the commutative property of multiplication.

$7 \cdot 5 x^{3} x^{2} + 7 \cdot 3 x^{3} x + 7 x^{3} \cdot 1$

Multiply $7$ by $1$ .

$7 \cdot 5 x^{3} x^{2} + 7 \cdot 3 x^{3} x + 7 x^{3}$

Simplify each term.

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

Move $x^{2}$ .

$7 \cdot 5 (x^{2} x^{3}) + 7 \cdot 3 x^{3} x + 7 x^{3}$

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

$7 \cdot 5 x^{2 + 3} + 7 \cdot 3 x^{3} x + 7 x^{3}$

Add $2$ and $3$ .

$7 \cdot 5 x^{5} + 7 \cdot 3 x^{3} x + 7 x^{3}$

Multiply $7$ by $5$ .

$35 x^{5} + 7 \cdot 3 x^{3} x + 7 x^{3}$

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

Move $x$ .

$35 x^{5} + 7 \cdot 3 (x \cdot x^{3}) + 7 x^{3}$

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

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

$35 x^{5} + 7 \cdot 3 (x^{1} x^{3}) + 7 x^{3}$

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

$35 x^{5} + 7 \cdot 3 x^{1 + 3} + 7 x^{3}$

Add $1$ and $3$ .

$35 x^{5} + 7 \cdot 3 x^{4} + 7 x^{3}$

Multiply $7$ by $3$ .

$35 x^{5} + 21 x^{4} + 7 x^{3}$