Calculus Examples

$27 r^{3} - 64 s^{3}$

Step 1

Rewrite $27 r^{3}$ as ${(3 r)}^{3}$ .

${(3 r)}^{3} - 64 s^{3}$

Step 2

Rewrite $64 s^{3}$ as ${(4 s)}^{3}$ .

${(3 r)}^{3} - {(4 s)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 3 r$ and $b = 4 s$ .

$(3 r - (4 s)) ({(3 r)}^{2} + 3 r (4 s) + {(4 s)}^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Multiply $4$ by $- 1$ .

$(3 r - 4 s) ({(3 r)}^{2} + 3 r (4 s) + {(4 s)}^{2})$

Step 4.2

Apply the product rule to $3 r$ .

$(3 r - 4 s) (3^{2} r^{2} + 3 r (4 s) + {(4 s)}^{2})$

Step 4.3

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

$(3 r - 4 s) (9 r^{2} + 3 r (4 s) + {(4 s)}^{2})$

Step 4.4

Rewrite using the commutative property of multiplication.

$(3 r - 4 s) (9 r^{2} + 3 \cdot 4 r s + {(4 s)}^{2})$

Step 4.5

Multiply $3$ by $4$ .

$(3 r - 4 s) (9 r^{2} + 12 r s + {(4 s)}^{2})$

Step 4.6

Apply the product rule to $4 s$ .

$(3 r - 4 s) (9 r^{2} + 12 r s + 4^{2} s^{2})$

Step 4.7

Raise $4$ to the power of $2$ .

$(3 r - 4 s) (9 r^{2} + 12 r s + 16 s^{2})$