Algebra Examples

$x (x - y) + y (y - x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $x$ by $x$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $y$ by $y$ .

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

Step 1.6

Rewrite using the commutative property of multiplication.

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

Step 2

Subtract $y x$ from $- x y$ .

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Step 2.1

Move $y$ .

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

Step 2.2

Subtract $x y$ from $- x y$ .

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