Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Expand $(x + y) (x + y)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.3.1.2

Multiply $y$ by $y$ .

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

Step 1.3.2

Add $x y$ and $y x$ .

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Step 1.3.2.1

Reorder $y$ and $x$ .

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

Step 1.3.2.2

Add $x y$ and $x y$ .

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

Step 1.4

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

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

Step 1.5

Expand $(x - y) (x - y)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $x$ by $x$ .

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

Step 1.6.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.4

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

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Step 1.6.1.4.1

Move $y$ .

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

Step 1.6.1.4.2

Multiply $y$ by $y$ .

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

Step 1.6.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.6.1.6

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

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

Step 1.6.2

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

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Step 1.6.2.1

Move $y$ .

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

Step 1.6.2.2

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

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

Subtract $2 x y$ from $2 x y$ .

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

Step 2.1.2

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

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

Step 2.2

Add $x^{2}$ and $x^{2}$ .

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

Step 2.3

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

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Step 2.3.1

Subtract $2 x^{2}$ from $2 x^{2}$ .

$y^{2} + y^{2} + 0$

Step 2.3.2

Add $y^{2} + y^{2}$ and $0$ .

$y^{2} + y^{2}$

Step 2.4

Add $y^{2}$ and $y^{2}$ .

$2 y^{2}$