Algebra Examples

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

Step 1

Rewrite ${(x + 1 - y)}^{2}$ as $(x + 1 - y) (x + 1 - y)$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Multiply $x$ by $1$ .

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

Step 3.1.3

Rewrite using the commutative property of multiplication.

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

Step 3.1.4

Multiply $x$ by $1$ .

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

Step 3.1.5

Multiply $1$ by $1$ .

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

Step 3.1.6

Multiply $- y$ by $1$ .

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

Step 3.1.7

Multiply $- 1$ by $1$ .

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

Step 3.1.8

Rewrite using the commutative property of multiplication.

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

Step 3.1.9

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

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Step 3.1.9.1

Move $y$ .

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

Step 3.1.9.2

Multiply $y$ by $y$ .

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

Step 3.1.10

Multiply $- 1$ by $- 1$ .

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

Step 3.1.11

Multiply $y^{2}$ by $1$ .

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

Step 3.2

Add $x$ and $x$ .

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

Step 4

Subtract $y x$ from $- x y$ .

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Step 4.1

Move $y$ .

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

Step 4.2

Subtract $x y$ from $- x y$ .

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

Step 5

Subtract $y$ from $- y$ .

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

Step 6

Reorder.

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Step 6.1

Move $1$ .

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

Step 6.2

Move $- 2 y$ .

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

Step 6.3

Move $2 x$ .

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