Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $- 1$ by $- 1$ .

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

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

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

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

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

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Step 1.4.1.1.1

Move $x$ .

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

Step 1.4.1.1.2

Multiply $x$ by $x$ .

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

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

Step 1.4.1.2

Multiply $- 2$ by $- 1$ .

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

Step 1.4.1.3

Multiply $x$ by $1$ .

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

Step 1.4.1.4

Multiply $- 2$ by $1$ .

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

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

Step 1.4.2

Add $2 x$ and $x$ .

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

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Add $x$ and $3 x$ .

$4 x - y - x^{2} - 2$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $4 x$ .

$- y - x^{2} + 4 x - 2$

Step 2.2.2

Reorder $- y$ and $- x^{2}$ .

$- x^{2} - y + 4 x - 2$

$- x^{2} - y + 4 x - 2$

$- x^{2} - y + 4 x - 2$

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