Algebra Examples

$\sqrt{25 {(x + 2)}^{4}}$

Step 1

Rewrite $25 {(x + 2)}^{4}$ as ${(5 {(x + 2)}^{2})}^{2}$ .

$\sqrt{{(5 {(x + 2)}^{2})}^{2}}$

Step 2

Pull terms out from under the radical.

$| 5 {(x + 2)}^{2} |$

Step 3

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

$| 5 ((x + 2) (x + 2)) |$

Step 4

Expand $(x + 2) (x + 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$| 5 (x (x + 2) + 2 (x + 2)) |$

Step 4.2

Apply the distributive property.

$| 5 (x \cdot x + x \cdot 2 + 2 (x + 2)) |$

Step 4.3

Apply the distributive property.

$| 5 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) |$

$| 5 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) |$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x$ by $x$ .

$| 5 (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) |$

Step 5.1.2

Move $2$ to the left of $x$ .

$| 5 (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) |$

Step 5.1.3

Multiply $2$ by $2$ .

$| 5 (x^{2} + 2 x + 2 x + 4) |$

$| 5 (x^{2} + 2 x + 2 x + 4) |$

Step 5.2

Add $2 x$ and $2 x$ .

$| 5 (x^{2} + 4 x + 4) |$

$| 5 (x^{2} + 4 x + 4) |$

Step 6

Apply the distributive property.

$| 5 x^{2} + 5 (4 x) + 5 \cdot 4 |$

Step 7

Simplify.

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Step 7.1

Multiply $4$ by $5$ .

$| 5 x^{2} + 20 x + 5 \cdot 4 |$

Step 7.2

Multiply $5$ by $4$ .

$| 5 x^{2} + 20 x + 20 |$

$| 5 x^{2} + 20 x + 20 |$

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