Algebra Examples

$G = a (4 - d^{2})$

Step 1

Rewrite the equation as $a (4 - d^{2}) = G$ .

$a (4 - d^{2}) = G$

Step 2

Divide each term in $a (4 - d^{2}) = G$ by $4 - d^{2}$ and simplify.

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Step 2.1

Divide each term in $a (4 - d^{2}) = G$ by $4 - d^{2}$ .

$\frac{a (4 - d^{2})}{4 - d^{2}} = \frac{G}{4 - d^{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4 - d^{2}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a (4 - d^{2})}{4 - d^{2}} = \frac{G}{4 - d^{2}}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{G}{4 - d^{2}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the denominator.

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Step 2.3.1.1

Rewrite $4$ as $2^{2}$ .

$a = \frac{G}{2^{2} - d^{2}}$

Step 2.3.1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = d$ .

$a = \frac{G}{(2 + d) (2 - d)}$