Simplify (2x+y)(x-4y)

$(2 x + y) (x - 4 y)$

Step 1

Expand $(2 x + y) (x - 4 y)$ using the FOIL Method.

Apply the distributive property.

$2 x (x - 4 y) + y (x - 4 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (- 4 y) + y (x - 4 y)$

Apply the distributive property.

$2 x \cdot x + 2 x (- 4 y) + y x + y (- 4 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$2 (x \cdot x) + 2 x (- 4 y) + y x + y (- 4 y)$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x (- 4 y) + y x + y (- 4 y)$

Rewrite using the commutative property of multiplication.

$2 x^{2} + 2 \cdot - 4 x y + y x + y (- 4 y)$

Multiply $2$ by $- 4$ .

$2 x^{2} - 8 x y + y x + y (- 4 y)$

Rewrite using the commutative property of multiplication.

$2 x^{2} - 8 x y + y x - 4 y \cdot y$

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

Move $y$ .

$2 x^{2} - 8 x y + y x - 4 (y \cdot y)$

Multiply $y$ by $y$ .

$2 x^{2} - 8 x y + y x - 4 y^{2}$

Add $- 8 x y$ and $y x$ .

Reorder $y$ and $x$ .

$2 x^{2} - 8 x y + x y - 4 y^{2}$

Add $- 8 x y$ and $x y$ .

$2 x^{2} - 7 x y - 4 y^{2}$