Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Apply the distributive property.

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

Step 2.2.3

Apply the distributive property.

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

Step 2.3

Simplify and combine like terms.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Multiply $x$ by $x$ .

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

Step 2.3.1.2

Multiply $x$ by $1$ .

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

Step 2.3.1.3

Multiply $x$ by $1$ .

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

Step 2.3.1.4

Multiply $1$ by $1$ .

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

Step 2.3.2

Add $x$ and $x$ .

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

Step 2.4

Apply the distributive property.

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

Step 2.5

Simplify.

Tap for more steps...

Step 2.5.1

Multiply $2$ by $- 1$ .

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

Step 2.5.2

Multiply $- 1$ by $1$ .

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

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $- x^{2} - 2 x - 1 + x + 1 + 1$ .

Tap for more steps...

Step 3.1.1

Add $- 1$ and $1$ .

$- x^{2} - 2 x + x + 0 + 1$

Step 3.1.2

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

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

Step 3.2

Add $- 2 x$ and $x$ .

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