Basic Math Examples

{(9 x + 2)}^{3}

${(9 x + 2)}^{3}$

Step 1

Use the Binomial Theorem.

{(9 x)}^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

${(9 x)}^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to

9 x

$9 x$ .

9^{3} x^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

$9^{3} x^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.2

Raise

9

$9$ to the power of

3

$3$ .

729 x^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

$729 x^{3} + 3 {(9 x)}^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.3

Apply the product rule to

9 x

$9 x$ .

729 x^{3} + 3 (9^{2} x^{2}) \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

$729 x^{3} + 3 (9^{2} x^{2}) \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.4

Raise

9

$9$ to the power of

2

$2$ .

729 x^{3} + 3 (81 x^{2}) \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

$729 x^{3} + 3 (81 x^{2}) \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.5

Multiply

81

$81$ by

3

$3$ .

729 x^{3} + 243 x^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}

$729 x^{3} + 243 x^{2} \cdot 2 + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.6

Multiply

2

$2$ by

243

$243$ .

729 x^{3} + 486 x^{2} + 3 (9 x) \cdot 2^{2} + 2^{3}

$729 x^{3} + 486 x^{2} + 3 (9 x) \cdot 2^{2} + 2^{3}$

Step 2.7

Multiply

9

$9$ by

3

$3$ .

729 x^{3} + 486 x^{2} + 27 x \cdot 2^{2} + 2^{3}

$729 x^{3} + 486 x^{2} + 27 x \cdot 2^{2} + 2^{3}$

Step 2.8

Raise

2

$2$ to the power of

2

$2$ .

729 x^{3} + 486 x^{2} + 27 x \cdot 4 + 2^{3}

$729 x^{3} + 486 x^{2} + 27 x \cdot 4 + 2^{3}$

Step 2.9

Multiply

4

$4$ by

27

$27$ .

729 x^{3} + 486 x^{2} + 108 x + 2^{3}

$729 x^{3} + 486 x^{2} + 108 x + 2^{3}$

Step 2.10

Raise

2

$2$ to the power of

3

$3$ .

729 x^{3} + 486 x^{2} + 108 x + 8

$729 x^{3} + 486 x^{2} + 108 x + 8$

729 x^{3} + 486 x^{2} + 108 x + 8

$729 x^{3} + 486 x^{2} + 108 x + 8$