Algebra Examples

2 {(x + y)}^{2} + (x + y) - 6

$2 {(x + y)}^{2} + (x + y) - 6$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Rewrite

{(x + y)}^{2}

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

(x + y) (x + y)

$(x + y) (x + y)$ .

2 ((x + y) (x + y)) + x + y - 6

$2 ((x + y) (x + y)) + x + y - 6$

Step 3

Expand

(x + y) (x + y)

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

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Step 3.1

Apply the distributive property.

2 (x (x + y) + y (x + y)) + x + y - 6

$2 (x (x + y) + y (x + y)) + x + y - 6$

Step 3.2

Apply the distributive property.

2 (x \cdot x + x y + y (x + y)) + x + y - 6

$2 (x \cdot x + x y + y (x + y)) + x + y - 6$

Step 3.3

Apply the distributive property.

2 (x \cdot x + x y + y x + y \cdot y) + x + y - 6

$2 (x \cdot x + x y + y x + y \cdot y) + x + y - 6$

2 (x \cdot x + x y + y x + y \cdot y) + x + y - 6

$2 (x \cdot x + x y + y x + y \cdot y) + x + y - 6$

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

$x$ by

x

$x$ .

2 (x^{2} + x y + y x + y \cdot y) + x + y - 6

$2 (x^{2} + x y + y x + y \cdot y) + x + y - 6$

Step 4.1.2

Multiply

y

$y$ by

y

$y$ .

2 (x^{2} + x y + y x + y^{2}) + x + y - 6

$2 (x^{2} + x y + y x + y^{2}) + x + y - 6$

2 (x^{2} + x y + y x + y^{2}) + x + y - 6

$2 (x^{2} + x y + y x + y^{2}) + x + y - 6$

Step 4.2

Add

x y

$x y$ and

y x

$y x$ .

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Step 4.2.1

Reorder

y

$y$ and

x

$x$ .

2 (x^{2} + x y + x y + y^{2}) + x + y - 6

$2 (x^{2} + x y + x y + y^{2}) + x + y - 6$

Step 4.2.2

Add

x y

$x y$ and

x y

$x y$ .

2 (x^{2} + 2 x y + y^{2}) + x + y - 6

$2 (x^{2} + 2 x y + y^{2}) + x + y - 6$

2 (x^{2} + 2 x y + y^{2}) + x + y - 6

$2 (x^{2} + 2 x y + y^{2}) + x + y - 6$

2 (x^{2} + 2 x y + y^{2}) + x + y - 6

$2 (x^{2} + 2 x y + y^{2}) + x + y - 6$

Step 5

Apply the distributive property.

2 x^{2} + 2 (2 x y) + 2 y^{2} + x + y - 6

$2 x^{2} + 2 (2 x y) + 2 y^{2} + x + y - 6$

Step 6

Multiply

2

$2$ by

2

$2$ .

2 x^{2} + 4 (x y) + 2 y^{2} + x + y - 6

$2 x^{2} + 4 (x y) + 2 y^{2} + x + y - 6$

Step 7

Remove parentheses.

2 x^{2} + 4 x y + 2 y^{2} + x + y - 6

$2 x^{2} + 4 x y + 2 y^{2} + x + y - 6$