Basic Math Examples

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

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

Subtract $a^{2}$ from both sides of the equation.

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

Step 4

Divide each term in $- b^{2} = 39 - a^{2}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- b^{2} = 39 - a^{2}$ by $- 1$ .

$\frac{- b^{2}}{- 1} = \frac{39}{- 1} + \frac{- a^{2}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{b^{2}}{1} = \frac{39}{- 1} + \frac{- a^{2}}{- 1}$

Step 4.2.2

Divide $b^{2}$ by $1$ .

$b^{2} = \frac{39}{- 1} + \frac{- a^{2}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $39$ by $- 1$ .

$b^{2} = - 39 + \frac{- a^{2}}{- 1}$

Step 4.3.1.2

Dividing two negative values results in a positive value.

$b^{2} = - 39 + \frac{a^{2}}{1}$

Step 4.3.1.3

Divide $a^{2}$ by $1$ .

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

Step 5

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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

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

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

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