Basic Math Examples

${(4 a - 4 b)}^{3}$

Step 1

Use the Binomial Theorem.

${(4 a)}^{3} + 3 {(4 a)}^{2} (- 4 b) + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $4 a$ .

$4^{3} a^{3} + 3 {(4 a)}^{2} (- 4 b) + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.2

Raise $4$ to the power of $3$ .

$64 a^{3} + 3 {(4 a)}^{2} (- 4 b) + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.3

Rewrite using the commutative property of multiplication.

$64 a^{3} + 3 \cdot - 4 {(4 a)}^{2} b + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.4

Multiply $3$ by $- 4$ .

$64 a^{3} - 12 {(4 a)}^{2} b + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.5

Apply the product rule to $4 a$ .

$64 a^{3} - 12 (4^{2} a^{2}) b + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.6

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

$64 a^{3} - 12 (16 a^{2}) b + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.7

Multiply $16$ by $- 12$ .

$64 a^{3} - 192 a^{2} b + 3 (4 a) {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.8

Multiply $4$ by $3$ .

$64 a^{3} - 192 a^{2} b + 12 a {(- 4 b)}^{2} + {(- 4 b)}^{3}$

Step 2.9

Apply the product rule to $- 4 b$ .

$64 a^{3} - 192 a^{2} b + 12 a ({(- 4)}^{2} b^{2}) + {(- 4 b)}^{3}$

Step 2.10

Rewrite using the commutative property of multiplication.

$64 a^{3} - 192 a^{2} b + 12 \cdot {(- 4)}^{2} a b^{2} + {(- 4 b)}^{3}$

Step 2.11

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

$64 a^{3} - 192 a^{2} b + 12 \cdot 16 a b^{2} + {(- 4 b)}^{3}$

Step 2.12

Multiply $12$ by $16$ .

$64 a^{3} - 192 a^{2} b + 192 a b^{2} + {(- 4 b)}^{3}$

Step 2.13

Apply the product rule to $- 4 b$ .

$64 a^{3} - 192 a^{2} b + 192 a b^{2} + {(- 4)}^{3} b^{3}$

Step 2.14

Raise $- 4$ to the power of $3$ .

$64 a^{3} - 192 a^{2} b + 192 a b^{2} - 64 b^{3}$