Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

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

$2 ((x + y) (x + y)) + x + y - 3$

Step 3

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

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Step 3.1

Apply the distributive property.

$2 (x (x + y) + y (x + y)) + x + y - 3$

Step 3.2

Apply the distributive property.

$2 (x \cdot x + x y + y (x + y)) + x + y - 3$

Step 3.3

Apply the distributive property.

$2 (x \cdot x + x y + y x + y \cdot y) + x + y - 3$

$2 (x \cdot x + x y + y x + y \cdot y) + x + y - 3$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

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

Step 4.1.2

Multiply $y$ by $y$ .

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

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

Step 4.2

Add $x y$ and $y x$ .

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Step 4.2.1

Reorder $y$ and $x$ .

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

Step 4.2.2

Add $x y$ and $x y$ .

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

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

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $2$ by $2$ .

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

Step 7

Remove parentheses.

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

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