Simplify (x+1)^2-x^2

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

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

Add $x$ and $x$ .

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

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

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

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

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

$2 x + 1 + 0$

Add $2 x + 1$ and $0$ .

$2 x + 1$

$2 x + 1$

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