Algebra Examples

$(x + 1) (x + 4) = 8$

Step 1

Subtract $8$ from both sides of the equation.

$(x + 1) (x + 4) - 8 = 0$

Step 2

Simplify $(x + 1) (x + 4) - 8$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$x (x + 4) + 1 (x + 4) - 8 = 0$

Step 2.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 4 + 1 (x + 4) - 8 = 0$

Step 2.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 4 + 1 x + 1 \cdot 4 - 8 = 0$

$x \cdot x + x \cdot 4 + 1 x + 1 \cdot 4 - 8 = 0$

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 $x$ .

$x^{2} + x \cdot 4 + 1 x + 1 \cdot 4 - 8 = 0$

Step 2.1.2.1.2

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x + 1 x + 1 \cdot 4 - 8 = 0$

Step 2.1.2.1.3

Multiply $x$ by $1$ .

$x^{2} + 4 x + x + 1 \cdot 4 - 8 = 0$

Step 2.1.2.1.4

Multiply $4$ by $1$ .

$x^{2} + 4 x + x + 4 - 8 = 0$

$x^{2} + 4 x + x + 4 - 8 = 0$

Step 2.1.2.2

Add $4 x$ and $x$ .

$x^{2} + 5 x + 4 - 8 = 0$

$x^{2} + 5 x + 4 - 8 = 0$

$x^{2} + 5 x + 4 - 8 = 0$

Step 2.2

Subtract $8$ from $4$ .

$x^{2} + 5 x - 4 = 0$

$x^{2} + 5 x - 4 = 0$

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 $x^{2} + 5 x - 4$ .

$x^{2} + 5 x - 4 = 0$

Step 5

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