Algebra Examples

$a^{2} - b^{2} = 0$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

$b^{2} = \frac{a^{2}}{1}$

Step 2.3.2

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

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

Step 3

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| b | = | a |$

Step 4

Solve for $b$ .

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Step 4.1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$b = \pm | a |$

Step 4.2

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

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Step 4.2.1

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

$b = | a |$

Step 4.2.2

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

$b = - | a |$

Step 4.2.3

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

$b = | a |$

$b = - | a |$

$b = | a |$

$b = - | a |$

$b = | a |$

$b = - | a |$