Calculus Examples

$a = {(7 - 2 b)}^{3}$

Step 1

Use the Binomial Theorem.

$a = 7^{3} + 3 \cdot 7^{2} (- 2 b) + 3 \cdot 7 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $7$ to the power of $3$ .

$a = 343 + 3 \cdot 7^{2} (- 2 b) + 3 \cdot 7 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2.1.2

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

$a = 343 + 3 \cdot 49 (- 2 b) + 3 \cdot 7 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2.1.3

Multiply $3$ by $49$ .

$a = 343 + 147 (- 2 b) + 3 \cdot 7 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2.1.4

Multiply $- 2$ by $147$ .

$a = 343 - 294 b + 3 \cdot 7 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2.1.5

Multiply $3$ by $7$ .

$a = 343 - 294 b + 21 {(- 2 b)}^{2} + {(- 2 b)}^{3}$

Step 2.1.6

Apply the product rule to $- 2 b$ .

$a = 343 - 294 b + 21 ({(- 2)}^{2} b^{2}) + {(- 2 b)}^{3}$

Step 2.1.7

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

$a = 343 - 294 b + 21 (4 b^{2}) + {(- 2 b)}^{3}$

Step 2.1.8

Multiply $4$ by $21$ .

$a = 343 - 294 b + 84 b^{2} + {(- 2 b)}^{3}$

Step 2.1.9

Apply the product rule to $- 2 b$ .

$a = 343 - 294 b + 84 b^{2} + {(- 2)}^{3} b^{3}$

Step 2.1.10

Raise $- 2$ to the power of $3$ .

$a = 343 - 294 b + 84 b^{2} - 8 b^{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $343$ .

$a = - 294 b + 84 b^{2} - 8 b^{3} + 343$

Step 2.2.2

Move $- 294 b$ .

$a = 84 b^{2} - 8 b^{3} - 294 b + 343$

Step 2.2.3

Reorder $84 b^{2}$ and $- 8 b^{3}$ .

$a = - 8 b^{3} + 84 b^{2} - 294 b + 343$