Basic Math Examples

${(3 a + 2)}^{5}$

Step 1

Use the Binomial Theorem.

${(3 a)}^{5} + 5 {(3 a)}^{4} \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the product rule to $3 a$ .

$3^{5} a^{5} + 5 {(3 a)}^{4} \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.2

Raise $3$ to the power of $5$ .

$243 a^{5} + 5 {(3 a)}^{4} \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.3

Apply the product rule to $3 a$ .

$243 a^{5} + 5 (3^{4} a^{4}) \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.4

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

$243 a^{5} + 5 (81 a^{4}) \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.5

Multiply $81$ by $5$ .

$243 a^{5} + 405 a^{4} \cdot 2 + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.6

Multiply $2$ by $405$ .

$243 a^{5} + 810 a^{4} + 10 {(3 a)}^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.7

Apply the product rule to $3 a$ .

$243 a^{5} + 810 a^{4} + 10 (3^{3} a^{3}) \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.8

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

$243 a^{5} + 810 a^{4} + 10 (27 a^{3}) \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.9

Multiply $27$ by $10$ .

$243 a^{5} + 810 a^{4} + 270 a^{3} \cdot 2^{2} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.10

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

$243 a^{5} + 810 a^{4} + 270 a^{3} \cdot 4 + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.11

Multiply $4$ by $270$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 10 {(3 a)}^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.12

Apply the product rule to $3 a$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 10 (3^{2} a^{2}) \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.13

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

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 10 (9 a^{2}) \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.14

Multiply $9$ by $10$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 90 a^{2} \cdot 2^{3} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.15

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

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 90 a^{2} \cdot 8 + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.16

Multiply $8$ by $90$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 720 a^{2} + 5 (3 a) \cdot 2^{4} + 2^{5}$

Step 2.17

Multiply $3$ by $5$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 720 a^{2} + 15 a \cdot 2^{4} + 2^{5}$

Step 2.18

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

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 720 a^{2} + 15 a \cdot 16 + 2^{5}$

Step 2.19

Multiply $16$ by $15$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 720 a^{2} + 240 a + 2^{5}$

Step 2.20

Raise $2$ to the power of $5$ .

$243 a^{5} + 810 a^{4} + 1080 a^{3} + 720 a^{2} + 240 a + 32$