Evaluate (x+y)^2=x^2+y^2

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

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $y$ by $y$ .

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

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

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

Add $x y$ and $x y$ .

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

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

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

$2 x y + y^{2} + 0 = y^{2}$

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

$2 x y + y^{2} = y^{2}$

Move all terms not containing $x$ to the right side of the equation.

Subtract $y^{2}$ from both sides of the equation.

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

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

$2 x y = 0$

Divide each term in $2 x y = 0$ by $2 y$ and simplify.

Divide each term in $2 x y = 0$ by $2 y$ .

$\frac{2 x y}{2 y} = \frac{0}{2 y}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x y}{2 y} = \frac{0}{2 y}$

Rewrite the expression.

$\frac{x y}{y} = \frac{0}{2 y}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{x y}{y} = \frac{0}{2 y}$

Divide $x$ by $1$ .

$x = \frac{0}{2 y}$

Simplify the right side.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

$x = \frac{2 (0)}{2 y}$

Cancel the common factors.

Factor $2$ out of $2 y$ .

$x = \frac{2 (0)}{2 (y)}$

Cancel the common factor.

$x = \frac{2 \cdot 0}{2 y}$

Rewrite the expression.

$x = \frac{0}{y}$

Divide $0$ by $y$ .

$x = 0$

Evaluate (x+y)^2=x^2+y^2

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