Finite Math Examples

$(x + \frac{1}{2}) (x + \frac{7}{2})$

Step 1

Expand $(x + \frac{1}{2}) (x + \frac{7}{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x (x + \frac{7}{2}) + \frac{1}{2} (x + \frac{7}{2})$

Step 1.2

Apply the distributive property.

$x \cdot x + x \frac{7}{2} + \frac{1}{2} (x + \frac{7}{2})$

Step 1.3

Apply the distributive property.

$x \cdot x + x \frac{7}{2} + \frac{1}{2} x + \frac{1}{2} \cdot \frac{7}{2}$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \frac{7}{2} + \frac{1}{2} x + \frac{1}{2} \cdot \frac{7}{2}$

Step 2.1.2

Combine $x$ and $\frac{7}{2}$ .

$x^{2} + \frac{x \cdot 7}{2} + \frac{1}{2} x + \frac{1}{2} \cdot \frac{7}{2}$

Step 2.1.3

Move $7$ to the left of $x$ .

$x^{2} + \frac{7 \cdot x}{2} + \frac{1}{2} x + \frac{1}{2} \cdot \frac{7}{2}$

Step 2.1.4

Combine $\frac{1}{2}$ and $x$ .

$x^{2} + \frac{7 x}{2} + \frac{x}{2} + \frac{1}{2} \cdot \frac{7}{2}$

Step 2.1.5

Multiply $\frac{1}{2} \cdot \frac{7}{2}$ .

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Step 2.1.5.1

Multiply $\frac{1}{2}$ by $\frac{7}{2}$ .

$x^{2} + \frac{7 x}{2} + \frac{x}{2} + \frac{7}{2 \cdot 2}$

Step 2.1.5.2

Multiply $2$ by $2$ .

$x^{2} + \frac{7 x}{2} + \frac{x}{2} + \frac{7}{4}$

Step 2.2

Combine the numerators over the common denominator.

$x^{2} + \frac{7 x + x}{2} + \frac{7}{4}$

Step 3

Add $7 x$ and $x$ .

$x^{2} + \frac{8 x}{2} + \frac{7}{4}$

Step 4

Cancel the common factor of $8$ and $2$ .

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Step 4.1

Factor $2$ out of $8 x$ .

$x^{2} + \frac{2 (4 x)}{2} + \frac{7}{4}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (4 x)}{2 (1)} + \frac{7}{4}$

Step 4.2.2

Cancel the common factor.

$x^{2} + \frac{2 (4 x)}{2 \cdot 1} + \frac{7}{4}$

Step 4.2.3

Rewrite the expression.

$x^{2} + \frac{4 x}{1} + \frac{7}{4}$

Step 4.2.4

Divide $4 x$ by $1$ .

$x^{2} + 4 x + \frac{7}{4}$