Finite Math Examples

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

Step 1

Expand $(x + 1 - y) (x + 1 + y)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x \cdot x + x \cdot 1 + x y + 1 x + 1 \cdot 1 + 1 y - y x - y \cdot 1 - y \cdot y$ .

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Step 2.1.1

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

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

Step 2.1.2

Subtract $x y$ from $x y$ .

$x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 + 1 y + 0 - y \cdot 1 - y \cdot y$

Step 2.1.3

Add $x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 + 1 y$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Multiply $x$ by $1$ .

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

Step 2.2.3

Multiply $x$ by $1$ .

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

Step 2.2.4

Multiply $1$ by $1$ .

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

Step 2.2.5

Multiply $y$ by $1$ .

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

Step 2.2.6

Multiply $- 1$ by $1$ .

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

Step 2.2.7

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

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Step 2.2.7.1

Move $y$ .

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

Step 2.2.7.2

Multiply $y$ by $y$ .

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

Step 2.3

Simplify by adding terms.

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Step 2.3.1

Combine the opposite terms in $x^{2} + x + x + 1 + y - y - y^{2}$ .

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Step 2.3.1.1

Subtract $y$ from $y$ .

$x^{2} + x + x + 1 + 0 - y^{2}$

Step 2.3.1.2

Add $x^{2} + x + x + 1$ and $0$ .

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

Step 2.3.2

Add $x$ and $x$ .

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

Step 2.3.3

Reorder.

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Step 2.3.3.1

Move $1$ .

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

Step 2.3.3.2

Move $2 x$ .

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