Calculus Examples

$1000 c^{3} + 343$

Step 1

Rewrite $1000 c^{3}$ as ${(10 c)}^{3}$ .

${(10 c)}^{3} + 343$

Step 2

Rewrite $343$ as $7^{3}$ .

${(10 c)}^{3} + 7^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 10 c$ and $b = 7$ .

$(10 c + 7) ({(10 c)}^{2} - (10 c) \cdot 7 + 7^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the product rule to $10 c$ .

$(10 c + 7) (10^{2} c^{2} - (10 c) \cdot 7 + 7^{2})$

Step 4.2

Raise $10$ to the power of $2$ .

$(10 c + 7) (100 c^{2} - (10 c) \cdot 7 + 7^{2})$

Step 4.3

Multiply $10$ by $- 1$ .

$(10 c + 7) (100 c^{2} - 10 c \cdot 7 + 7^{2})$

Step 4.4

Multiply $7$ by $- 10$ .

$(10 c + 7) (100 c^{2} - 70 c + 7^{2})$

Step 4.5

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

$(10 c + 7) (100 c^{2} - 70 c + 49)$