Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.3.1.2

Multiply $y$ by $y$ .

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

Step 1.3.2

Add $x y$ and $y x$ .

Tap for more steps...

Step 1.3.2.1

Reorder $y$ and $x$ .

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

Step 1.3.2.2

Add $x y$ and $x y$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- - y^{2}$ .

Tap for more steps...

Step 1.5.1

Multiply $- 1$ by $- 1$ .

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

Step 1.5.2

Multiply $y^{2}$ by $1$ .

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

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

Subtract $x y$ from $2 x y$ .

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

Step 2.3

Multiply $x$ by $1$ .

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

Step 2.4

Add $y^{2}$ and $y^{2}$ .

$2 y^{2} + x y$