Finite Math Examples

$39 = 3 \cdot 13$ , $39 = (a + b) (a - b)$

Step 1

Rewrite the equation as $(a + b) (a - b) = 39$ .

$(a + b) (a - b) = 39$

Step 2

Simplify $(a + b) (a - b)$ .

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Step 2.1

Expand $(a + b) (a - b)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$a (a - b) + b (a - b) = 39$

Step 2.1.2

Apply the distributive property.

$a \cdot a + a (- b) + b (a - b) = 39$

Step 2.1.3

Apply the distributive property.

$a \cdot a + a (- b) + b a + b (- b) = 39$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in $a \cdot a + a (- b) + b a + b (- b)$ .

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Step 2.2.1.1

Reorder the factors in the terms $a (- b)$ and $b a$ .

$a \cdot a - a b + a b + b (- b) = 39$

Step 2.2.1.2

Add $- a b$ and $a b$ .

$a \cdot a + 0 + b (- b) = 39$

Step 2.2.1.3

Add $a \cdot a$ and $0$ .

$a \cdot a + b (- b) = 39$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply $a$ by $a$ .

$a^{2} + b (- b) = 39$

Step 2.2.2.2

Rewrite using the commutative property of multiplication.

$a^{2} - b \cdot b = 39$

Step 2.2.2.3

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.2.3.1

Move $b$ .

$a^{2} - (b \cdot b) = 39$

Step 2.2.2.3.2

Multiply $b$ by $b$ .

$a^{2} - b^{2} = 39$

Step 3

Add $b^{2}$ to both sides of the equation.

$a^{2} = 39 + b^{2}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{39 + b^{2}}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$a = \sqrt{39 + b^{2}}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$a = - \sqrt{39 + b^{2}}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$a = \sqrt{39 + b^{2}}$

$a = - \sqrt{39 + b^{2}}$

$a = \sqrt{39 + b^{2}}$

$a = - \sqrt{39 + b^{2}}$