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

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

Step 1

Simplify each term.

Rewrite ${(2 x - y)}^{2}$ as $(2 x - y) (2 x - y)$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 1$ by $- 1$ .

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

Multiply $y^{2}$ by $1$ .

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

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

Move $y$ .

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

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

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

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $3$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} - 3 x (- y) - y (3 x) - y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} - 3 \cdot - 1 x y - y (3 x) - y (- y)$

Multiply $- 3$ by $- 1$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - y (3 x) - y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 1 \cdot 3 y x - y (- y)$

Multiply $- 1$ by $3$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x - y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x - 1 \cdot - 1 y \cdot y$

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

Move $y$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x - 1 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x - 1 \cdot - 1 y^{2}$

Multiply $- 1$ by $- 1$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x + 1 y^{2}$

Multiply $y^{2}$ by $1$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 y x + y^{2}$

Subtract $3 y x$ from $3 x y$ .

Move $y$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 3 x y - 3 x y + y^{2}$

Subtract $3 x y$ from $3 x y$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + 0 + y^{2}$

Add $- 9 x^{2}$ and $0$ .

$4 x^{2} - 4 x y + y^{2} - 9 x^{2} + y^{2}$

Step 2

Simplify by adding terms.

Subtract $9 x^{2}$ from $4 x^{2}$ .

$- 5 x^{2} - 4 x y + y^{2} + y^{2}$

Add $y^{2}$ and $y^{2}$ .

$- 5 x^{2} - 4 x y + 2 y^{2}$

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

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