Basic Math Examples

$a {(- b + 3 c d)}^{2}$

Step 1

Factor $- 1$ out of $- b + 3 c d$ .

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Step 1.1

Reorder $- b$ and $3 c d$ .

$a {(3 c d - b)}^{2}$

Step 1.2

Factor $- 1$ out of $3 c d$ .

$a {(- (- 3 c d) - b)}^{2}$

Step 1.3

Factor $- 1$ out of $- b$ .

$a {(- (- 3 c d) - (b))}^{2}$

Step 1.4

Factor $- 1$ out of $- (- 3 c d) - (b)$ .

$a {(- (- 3 c d + b))}^{2}$

Step 2

Factor.

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Step 2.1

Apply the product rule to $- (- 3 c d + b)$ .

$a ({(- 1)}^{2} {(- 3 c d + b)}^{2})$

Step 2.2

Remove unnecessary parentheses.

$a {(- 1)}^{2} {(- 3 c d + b)}^{2}$

Step 3

Factor $- 1$ out of $- 3 c d + b$ .

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Step 3.1

Factor $- 1$ out of $- 3 c d$ .

$a {(- 1)}^{2} {(- (3 c d) + b)}^{2}$

Step 3.2

Factor $- 1$ out of $b$ .

$a {(- 1)}^{2} {(- (3 c d) - 1 (- b))}^{2}$

Step 3.3

Factor $- 1$ out of $- (3 c d) - 1 (- b)$ .

$a {(- 1)}^{2} {(- (3 c d - b))}^{2}$

Step 4

Factor.

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Step 4.1

Apply the product rule to $- (3 c d - b)$ .

$a {(- 1)}^{2} ({(- 1)}^{2} {(3 c d - b)}^{2})$

Step 4.2

Remove unnecessary parentheses.

$a {(- 1)}^{2} {(- 1)}^{2} {(3 c d - b)}^{2}$

Step 5

Multiply ${(- 1)}^{2}$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 5.1

Move ${(- 1)}^{2}$ .

$a ({(- 1)}^{2} {(- 1)}^{2}) {(3 c d - b)}^{2}$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a {(- 1)}^{2 + 2} {(3 c d - b)}^{2}$

Step 5.3

Add $2$ and $2$ .

$a {(- 1)}^{4} {(3 c d - b)}^{2}$