Algebra Examples

$2 x + (x - 4) (x + 1) = 9$

Step 1

Subtract $9$ from both sides of the equation.

$2 x + (x - 4) (x + 1) - 9 = 0$

Step 2

Simplify $2 x + (x - 4) (x + 1) - 9$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(x - 4) (x + 1)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$2 x + x (x + 1) - 4 (x + 1) - 9 = 0$

Step 2.1.1.2

Apply the distributive property.

$2 x + x \cdot x + x \cdot 1 - 4 (x + 1) - 9 = 0$

Step 2.1.1.3

Apply the distributive property.

$2 x + x \cdot x + x \cdot 1 - 4 x - 4 \cdot 1 - 9 = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $x$ by $x$ .

$2 x + x^{2} + x \cdot 1 - 4 x - 4 \cdot 1 - 9 = 0$

Step 2.1.2.1.2

Multiply $x$ by $1$ .

$2 x + x^{2} + x - 4 x - 4 \cdot 1 - 9 = 0$

Step 2.1.2.1.3

Multiply $- 4$ by $1$ .

$2 x + x^{2} + x - 4 x - 4 - 9 = 0$

Step 2.1.2.2

Subtract $4 x$ from $x$ .

$2 x + x^{2} - 3 x - 4 - 9 = 0$

Step 2.2

Subtract $3 x$ from $2 x$ .

$x^{2} - x - 4 - 9 = 0$

Step 2.3

Subtract $9$ from $- 4$ .

$x^{2} - x - 13 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $x^{2} - x - 13$ .

$x^{2} - x - 13 = 0$

Step 5