Basic Math Examples

{(u + 9)}^{8}

${(u + 9)}^{8}$

Step 1

Use the Binomial Theorem.

u^{8} + 8 u^{7} \cdot 9 + 28 u^{6} \cdot 9^{2} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 8 u^{7} \cdot 9 + 28 u^{6} \cdot 9^{2} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2

Simplify each term.

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Step 2.1

Multiply

9

$9$ by

8

$8$ .

u^{8} + 72 u^{7} + 28 u^{6} \cdot 9^{2} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 28 u^{6} \cdot 9^{2} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.2

Raise

9

$9$ to the power of

2

$2$ .

u^{8} + 72 u^{7} + 28 u^{6} \cdot 81 + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 28 u^{6} \cdot 81 + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.3

Multiply

81

$81$ by

28

$28$ .

u^{8} + 72 u^{7} + 2268 u^{6} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 2268 u^{6} + 56 u^{5} \cdot 9^{3} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.4

Raise

9

$9$ to the power of

3

$3$ .

u^{8} + 72 u^{7} + 2268 u^{6} + 56 u^{5} \cdot 729 + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 2268 u^{6} + 56 u^{5} \cdot 729 + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.5

Multiply

729

$729$ by

56

$56$ .

u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 70 u^{4} \cdot 9^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.6

Raise

9

$9$ to the power of

4

$4$ .

u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 70 u^{4} \cdot 6561 + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 70 u^{4} \cdot 6561 + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.7

Multiply

6561

$6561$ by

70

$70$ .

u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 56 u^{3} \cdot 9^{5} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.8

Raise

$9$ to the power of

$5$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 56 u^{3} \cdot 59049 + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.9

Multiply

$59049$ by

$56$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 28 u^{2} \cdot 9^{6} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.10

Raise

$9$ to the power of

$6$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 28 u^{2} \cdot 531441 + 8 u \cdot 9^{7} + 9^{8}$

Step 2.11

Multiply

$531441$ by

$28$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 14880348 u^{2} + 8 u \cdot 9^{7} + 9^{8}$

Step 2.12

Raise

$9$ to the power of

$7$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 14880348 u^{2} + 8 u \cdot 4782969 + 9^{8}$

Step 2.13

Multiply

$4782969$ by

$8$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 14880348 u^{2} + 38263752 u + 9^{8}$

Step 2.14

Raise

$9$ to the power of

$8$ .

$u^{8} + 72 u^{7} + 2268 u^{6} + 40824 u^{5} + 459270 u^{4} + 3306744 u^{3} + 14880348 u^{2} + 38263752 u + 43046721$