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

$(x + y) (x - y) - (x - 1) (x - 2)$

Step 1

Simplify each term.

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

Apply the distributive property.

$x (x - y) + y (x - y) - (x - 1) (x - 2)$

Apply the distributive property.

$x \cdot x + x (- y) + y (x - y) - (x - 1) (x - 2)$

Apply the distributive property.

$x \cdot x + x (- y) + y x + y (- y) - (x - 1) (x - 2)$

Combine the opposite terms in $x \cdot x + x (- y) + y x + y (- y)$ .

Reorder the factors in the terms $x (- y)$ and $y x$ .

$x \cdot x - x y + x y + y (- y) - (x - 1) (x - 2)$

Add $- x y$ and $x y$ .

$x \cdot x + 0 + y (- y) - (x - 1) (x - 2)$

Add $x \cdot x$ and $0$ .

$x \cdot x + y (- y) - (x - 1) (x - 2)$

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $- 1$ .

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

Expand $(- x + 1) (x - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 2$ by $1$ .

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

Add $2 x$ and $x$ .

$x^{2} - y^{2} - x^{2} + 3 x - 2$

Step 2

Combine the opposite terms in $x^{2} - y^{2} - x^{2} + 3 x - 2$ .

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

$- y^{2} + 0 + 3 x - 2$

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

$- y^{2} + 3 x - 2$

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

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