Find the Product (2x+y)(3x^2+y)

$(2 x + y) (3 x^{2} + y)$

Expand $(2 x + y) (3 x^{2} + y)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x^{2} + y) + y (3 x^{2} + y)$

Apply the distributive property.

$2 x (3 x^{2}) + 2 x y + y (3 x^{2} + y)$

Apply the distributive property.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $3$ .

$6 x^{3} + 2 x y + y (3 x^{2}) + y \cdot y$

Rewrite using the commutative property of multiplication.

$6 x^{3} + 2 x y + 3 y x^{2} + y \cdot y$

Multiply $y$ by $y$ .

$6 x^{3} + 2 x y + 3 y x^{2} + y^{2}$