Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Remove parentheses.

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

Step 1.2

Subtract $1$ from $2$ .

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

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Multiply $- 1$ by $- 1$ .

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

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

Step 1.4

Add $2$ and $1$ .

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

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.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x$ .

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

Step 3.1.2.2

Multiply $x$ by $x$ .

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

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

Step 3.1.3

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

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

Step 3.1.4

Multiply $- x$ by $1$ .

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

Step 3.1.5

Multiply $3$ by $1$ .

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

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

Step 3.2

Subtract $x$ from $3 x$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$