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

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

Step 1

Simplify terms.

Remove parentheses.

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

Subtract $1$ from $2$ .

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $- 1$ .

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

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

Add $2$ and $1$ .

$(x + 1) (- x + 3)$

$(x + 1) (- x + 3)$

Step 2

Expand $(x + 1) (- x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (- x + 3) + 1 (- x + 3)$

Apply the distributive property.

$x (- x) + x \cdot 3 + 1 (- x + 3)$

Apply the distributive property.

$x (- x) + x \cdot 3 + 1 (- x) + 1 \cdot 3$

$x (- x) + x \cdot 3 + 1 (- x) + 1 \cdot 3$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- x \cdot x + x \cdot 3 + 1 (- x) + 1 \cdot 3$

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

Move $x$ .

$- (x \cdot x) + x \cdot 3 + 1 (- x) + 1 \cdot 3$

Multiply $x$ by $x$ .

$- x^{2} + x \cdot 3 + 1 (- x) + 1 \cdot 3$

$- x^{2} + x \cdot 3 + 1 (- x) + 1 \cdot 3$

Move $3$ to the left of $x$ .

$- x^{2} + 3 \cdot x + 1 (- x) + 1 \cdot 3$

Multiply $- x$ by $1$ .

$- x^{2} + 3 x - x + 1 \cdot 3$

Multiply $3$ by $1$ .

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

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

Subtract $x$ from $3 x$ .

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

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

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