Simplify (2x+y)(x+3y)

$(2 x + y) (x + 3 y)$

Step 1

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

Apply the distributive property.

$2 x (x + 3 y) + y (x + 3 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (3 y) + y (x + 3 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (3 y) + y x + y (3 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$2 (x \cdot x) + 2 x (3 y) + y x + y (3 y)$

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Add $6 x y$ and $y x$ .

Reorder $y$ and $x$ .

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

Add $6 x y$ and $x y$ .

$2 x^{2} + 7 x y + 3 y^{2}$