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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$- y (- y) - y (3 x) - 3 x (- y) - 3 x (3 x)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 1 y \cdot y - y (3 x) - 3 x (- y) - 3 x (3 x)$

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

Move $y$ .

$- 1 \cdot - 1 (y \cdot y) - y (3 x) - 3 x (- y) - 3 x (3 x)$

Multiply $y$ by $y$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $3$ .

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

Add $- 3 y x$ and $3 x y$ .

Move $y$ .

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

Add $- 3 x y$ and $3 x y$ .

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

Add $y^{2}$ and $0$ .

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

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

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