Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Remove parentheses.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Multiply $- 1$ by $1$ .

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

Step 1.3

Simplify by adding and subtracting.

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Step 1.3.1

Subtract $1$ from $2$ .

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

Step 1.3.2

Add $2$ and $1$ .

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

Step 2

Expand $(x - y + 1) (x + y + 3)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x y + x \cdot 3 - y x - y \cdot y - y \cdot 3 + 1 x + 1 y + 1 \cdot 3$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x \cdot x + x y + x \cdot 3 - y x - y \cdot y - y \cdot 3 + 1 x + 1 y + 1 \cdot 3$ .

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Step 3.1.1

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

$x \cdot x + x y + x \cdot 3 - x y - y \cdot y - y \cdot 3 + 1 x + 1 y + 1 \cdot 3$

Step 3.1.2

Subtract $x y$ from $x y$ .

$x \cdot x + x \cdot 3 + 0 - y \cdot y - y \cdot 3 + 1 x + 1 y + 1 \cdot 3$

Step 3.1.3

Add $x \cdot x + x \cdot 3$ and $0$ .

$x \cdot x + x \cdot 3 - y \cdot y - y \cdot 3 + 1 x + 1 y + 1 \cdot 3$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

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

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

Step 3.2.3

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

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Step 3.2.3.1

Move $y$ .

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

Step 3.2.3.2

Multiply $y$ by $y$ .

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

Step 3.2.4

Multiply $3$ by $- 1$ .

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

Step 3.2.5

Multiply $x$ by $1$ .

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

Step 3.2.6

Multiply $y$ by $1$ .

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

Step 3.2.7

Multiply $3$ by $1$ .

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

Step 3.3

Simplify by adding terms.

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Step 3.3.1

Add $3 x$ and $x$ .

$x^{2} + 4 x - y^{2} - 3 y + y + 3$

Step 3.3.2

Add $- 3 y$ and $y$ .

$x^{2} + 4 x - y^{2} - 2 y + 3$

Step 3.3.3

Move $4 x$ .

$x^{2} - y^{2} + 4 x - 2 y + 3$