Simplify -(x+1)^2

$- {(x + 1)}^{2}$

Step 1

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$- ((x + 1) (x + 1))$

Step 2

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$- (x (x + 1) + 1 (x + 1))$

Apply the distributive property.

$- (x \cdot x + x \cdot 1 + 1 (x + 1))$

Apply the distributive property.

$- (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

$- (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

$- (x^{2} + x + x + 1)$

$- (x^{2} + x + x + 1)$

Add $x$ and $x$ .

$- (x^{2} + 2 x + 1)$

$- (x^{2} + 2 x + 1)$

Step 4

Apply the distributive property.

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

Step 5

Simplify.

Multiply $2$ by $- 1$ .

$- x^{2} - 2 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- x^{2} - 2 x - 1$

$- x^{2} - 2 x - 1$

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