Precalculus Examples

$d = {(\sqrt{{(2 a)}^{2} - (4 b)})}^{2} + (1 g) - {(7 b)}^{2}$

Step 1

Remove parentheses.

$d = {(\sqrt{{(2 a)}^{2} - (4 b)})}^{2} + 1 g - {(7 b)}^{2}$

Step 2

Remove parentheses.

$d = {\sqrt{{(2 a)}^{2} - 1 \cdot (4 b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 3

Remove parentheses.

$d = {(\sqrt{{(2 a)}^{2} - (4 b)})}^{2} + 1 g - {(7 b)}^{2}$

Step 4

Simplify ${(\sqrt{{(2 a)}^{2} - (4 b)})}^{2} + 1 g - {(7 b)}^{2}$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Apply the product rule to $2 a$ .

$d = {\sqrt{2^{2} a^{2} - (4 b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.2

Raise $2$ to the power of $2$ .

$d = {\sqrt{4 a^{2} - (4 b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.3

Multiply $4$ by $- 1$ .

$d = {\sqrt{4 a^{2} - 4 b}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.4

Factor $4$ out of $4 a^{2} - 4 b$ .

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Step 4.1.4.1

Factor $4$ out of $4 a^{2}$ .

$d = {\sqrt{4 (a^{2}) - 4 b}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.4.2

Factor $4$ out of $- 4 b$ .

$d = {\sqrt{4 (a^{2}) + 4 (- b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.4.3

Factor $4$ out of $4 (a^{2}) + 4 (- b)$ .

$d = {\sqrt{4 (a^{2} - b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.5

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

$d = {\sqrt{2^{2} (a^{2} - b)}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.6

Pull terms out from under the radical.

$d = {(2 \sqrt{a^{2} - b})}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.7

Apply the product rule to $2 \sqrt{a^{2} - b}$ .

$d = 2^{2} {\sqrt{a^{2} - b}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.8

Raise $2$ to the power of $2$ .

$d = 4 {\sqrt{a^{2} - b}}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.9

Rewrite ${\sqrt{a^{2} - b}}^{2}$ as $a^{2} - b$ .

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Step 4.1.9.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a^{2} - b}$ as ${(a^{2} - b)}^{\frac{1}{2}}$ .

$d = 4 {({(a^{2} - b)}^{\frac{1}{2}})}^{2} + 1 g - {(7 b)}^{2}$

Step 4.1.9.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d = 4 {(a^{2} - b)}^{\frac{1}{2} \cdot 2} + 1 g - {(7 b)}^{2}$

Step 4.1.9.3

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

$d = 4 {(a^{2} - b)}^{\frac{2}{2}} + 1 g - {(7 b)}^{2}$

Step 4.1.9.4

Cancel the common factor of $2$ .

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Step 4.1.9.4.1

Cancel the common factor.

$d = 4 {(a^{2} - b)}^{\frac{2}{2}} + 1 g - {(7 b)}^{2}$

Step 4.1.9.4.2

Rewrite the expression.

$d = 4 {(a^{2} - b)}^{1} + 1 g - {(7 b)}^{2}$

Step 4.1.9.5

Simplify.

$d = 4 (a^{2} - b) + 1 g - {(7 b)}^{2}$

Step 4.1.10

Apply the distributive property.

$d = 4 a^{2} + 4 (- b) + 1 g - {(7 b)}^{2}$

Step 4.1.11

Multiply $- 1$ by $4$ .

$d = 4 a^{2} - 4 b + 1 g - {(7 b)}^{2}$

Step 4.1.12

Multiply $g$ by $1$ .

$d = 4 a^{2} - 4 b + g - {(7 b)}^{2}$

Step 4.1.13

Apply the product rule to $7 b$ .

$d = 4 a^{2} - 4 b + g - (7^{2} b^{2})$

Step 4.1.14

Raise $7$ to the power of $2$ .

$d = 4 a^{2} - 4 b + g - (49 b^{2})$

Step 4.1.15

Multiply $49$ by $- 1$ .

$d = 4 a^{2} - 4 b + g - 49 b^{2}$

Step 4.2

Reorder.

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Step 4.2.1

Move $- 4 b$ .

$d = 4 a^{2} + g - 49 b^{2} - 4 b$

Step 4.2.2

Move $g$ .

$d = 4 a^{2} - 49 b^{2} + g - 4 b$