Algebra Examples

$\sqrt{{(x + 15)}^{4}}$

Step 1

Rewrite ${(x + 15)}^{4}$ as ${({(x + 15)}^{2})}^{2}$ .

$\sqrt{{({(x + 15)}^{2})}^{2}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

${(x + 15)}^{2}$

Step 3

Rewrite ${(x + 15)}^{2}$ as $(x + 15) (x + 15)$ .

$(x + 15) (x + 15)$

Step 4

Expand $(x + 15) (x + 15)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x (x + 15) + 15 (x + 15)$

Step 4.2

Apply the distributive property.

$x \cdot x + x \cdot 15 + 15 (x + 15)$

Step 4.3

Apply the distributive property.

$x \cdot x + x \cdot 15 + 15 x + 15 \cdot 15$

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 $x$ .

$x^{2} + x \cdot 15 + 15 x + 15 \cdot 15$

Step 5.1.2

Move $15$ to the left of $x$ .

$x^{2} + 15 \cdot x + 15 x + 15 \cdot 15$

Step 5.1.3

Multiply $15$ by $15$ .

$x^{2} + 15 x + 15 x + 225$

Step 5.2

Add $15 x$ and $15 x$ .

$x^{2} + 30 x + 225$