Simplify (2x-3y)(4x-y)

$(2 x - 3 y) (4 x - y)$

Step 1

Expand $(2 x - 3 y) (4 x - y)$ using the FOIL Method.

Apply the distributive property.

$2 x (4 x - y) - 3 y (4 x - y)$

Apply the distributive property.

$2 x (4 x) + 2 x (- y) - 3 y (4 x - y)$

Apply the distributive property.

$2 x (4 x) + 2 x (- y) - 3 y (4 x) - 3 y (- y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x \cdot x + 2 x (- y) - 3 y (4 x) - 3 y (- y)$

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

Move $x$ .

$2 \cdot 4 (x \cdot x) + 2 x (- y) - 3 y (4 x) - 3 y (- y)$

Multiply $x$ by $x$ .

$2 \cdot 4 x^{2} + 2 x (- y) - 3 y (4 x) - 3 y (- y)$

Multiply $2$ by $4$ .

$8 x^{2} + 2 x (- y) - 3 y (4 x) - 3 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} + 2 \cdot - 1 x y - 3 y (4 x) - 3 y (- y)$

Multiply $2$ by $- 1$ .

$8 x^{2} - 2 x y - 3 y (4 x) - 3 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 2 x y - 3 \cdot 4 y x - 3 y (- y)$

Multiply $- 3$ by $4$ .

$8 x^{2} - 2 x y - 12 y x - 3 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 2 x y - 12 y x - 3 \cdot - 1 y \cdot y$

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

Move $y$ .

$8 x^{2} - 2 x y - 12 y x - 3 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

$8 x^{2} - 2 x y - 12 y x - 3 \cdot - 1 y^{2}$

Multiply $- 3$ by $- 1$ .

$8 x^{2} - 2 x y - 12 y x + 3 y^{2}$

Subtract $12 y x$ from $- 2 x y$ .

Move $y$ .

$8 x^{2} - 2 x y - 12 x y + 3 y^{2}$

Subtract $12 x y$ from $- 2 x y$ .

$8 x^{2} - 14 x y + 3 y^{2}$