Find the Product (2x-y)(x+5y)

$(2 x - y) (x + 5 y)$

Step 1

Expand $(2 x - y) (x + 5 y)$ using the FOIL Method.

Apply the distributive property.

$2 x (x + 5 y) - y (x + 5 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (5 y) - y (x + 5 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (5 y) - y x - y (5 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$2 (x \cdot x) + 2 x (5 y) - y x - y (5 y)$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x (5 y) - y x - y (5 y)$

Rewrite using the commutative property of multiplication.

$2 x^{2} + 2 \cdot 5 x y - y x - y (5 y)$

Multiply $2$ by $5$ .

$2 x^{2} + 10 x y - y x - y (5 y)$

Rewrite using the commutative property of multiplication.

$2 x^{2} + 10 x y - y x - 1 \cdot 5 y \cdot y$

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

Move $y$ .

$2 x^{2} + 10 x y - y x - 1 \cdot 5 (y \cdot y)$

Multiply $y$ by $y$ .

$2 x^{2} + 10 x y - y x - 1 \cdot 5 y^{2}$

Multiply $- 1$ by $5$ .

$2 x^{2} + 10 x y - y x - 5 y^{2}$

Subtract $y x$ from $10 x y$ .

Move $y$ .

$2 x^{2} + 10 x y - 1 x y - 5 y^{2}$

Subtract $x y$ from $10 x y$ .

$2 x^{2} + 9 x y - 5 y^{2}$