Finite Math Examples

${(x + \frac{21}{2})}^{2}$

Step 1

Rewrite ${(x + \frac{21}{2})}^{2}$ as $(x + \frac{21}{2}) (x + \frac{21}{2})$ .

$(x + \frac{21}{2}) (x + \frac{21}{2})$

Step 2

Expand $(x + \frac{21}{2}) (x + \frac{21}{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x + \frac{21}{2}) + \frac{21}{2} (x + \frac{21}{2})$

Step 2.2

Apply the distributive property.

$x \cdot x + x \frac{21}{2} + \frac{21}{2} (x + \frac{21}{2})$

Step 2.3

Apply the distributive property.

$x \cdot x + x \frac{21}{2} + \frac{21}{2} x + \frac{21}{2} \cdot \frac{21}{2}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \frac{21}{2} + \frac{21}{2} x + \frac{21}{2} \cdot \frac{21}{2}$

Step 3.1.2

Combine $x$ and $\frac{21}{2}$ .

$x^{2} + \frac{x \cdot 21}{2} + \frac{21}{2} x + \frac{21}{2} \cdot \frac{21}{2}$

Step 3.1.3

Move $21$ to the left of $x$ .

$x^{2} + \frac{21 \cdot x}{2} + \frac{21}{2} x + \frac{21}{2} \cdot \frac{21}{2}$

Step 3.1.4

Combine $\frac{21}{2}$ and $x$ .

$x^{2} + \frac{21 x}{2} + \frac{21 x}{2} + \frac{21}{2} \cdot \frac{21}{2}$

Step 3.1.5

Multiply $\frac{21}{2} \cdot \frac{21}{2}$ .

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Step 3.1.5.1

Multiply $\frac{21}{2}$ by $\frac{21}{2}$ .

$x^{2} + \frac{21 x}{2} + \frac{21 x}{2} + \frac{21 \cdot 21}{2 \cdot 2}$

Step 3.1.5.2

Multiply $21$ by $21$ .

$x^{2} + \frac{21 x}{2} + \frac{21 x}{2} + \frac{441}{2 \cdot 2}$

Step 3.1.5.3

Multiply $2$ by $2$ .

$x^{2} + \frac{21 x}{2} + \frac{21 x}{2} + \frac{441}{4}$

Step 3.2

Add $\frac{21 x}{2}$ and $\frac{21 x}{2}$ .

$x^{2} + 2 \frac{21 x}{2} + \frac{441}{4}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$x^{2} + 2 \frac{21 x}{2} + \frac{441}{4}$

Step 4.2

Rewrite the expression.

$x^{2} + 21 x + \frac{441}{4}$