Simplify -(x+y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $y$ by $y$ .

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

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

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

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

Add $x y$ and $x y$ .

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

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2$ by $- 1$ .

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

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