Algebra Examples

${(3 x + 1)}^{3}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Use the Binomial Theorem.

${(3 x)}^{3} + 3 {(3 x)}^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the product rule to $3 x$ .

$3^{3} x^{3} + 3 {(3 x)}^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.2

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

$27 x^{3} + 3 {(3 x)}^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.3

Apply the product rule to $3 x$ .

$27 x^{3} + 3 (3^{2} x^{2}) \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.4

Multiply $3$ by $3^{2}$ by adding the exponents.

Tap for more steps...

Step 3.4.1

Move $3^{2}$ .

$27 x^{3} + 3^{2} \cdot 3 x^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.4.2

Multiply $3^{2}$ by $3$ .

Tap for more steps...

Step 3.4.2.1

Raise $3$ to the power of $1$ .

$27 x^{3} + 3^{2} \cdot 3^{1} x^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$27 x^{3} + 3^{2 + 1} x^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.4.3

Add $2$ and $1$ .

$27 x^{3} + 3^{3} x^{2} \cdot 1 + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.5

Simplify $3^{3} x^{2} \cdot 1$ .

$27 x^{3} + 3^{3} x^{2} + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.6

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

$27 x^{3} + 27 x^{2} + 3 (3 x) \cdot 1^{2} + 1^{3}$

Step 3.7

Multiply $3$ by $3$ .

$27 x^{3} + 27 x^{2} + 9 x \cdot 1^{2} + 1^{3}$

Step 3.8

One to any power is one.

$27 x^{3} + 27 x^{2} + 9 x \cdot 1 + 1^{3}$

Step 3.9

Multiply $9$ by $1$ .

$27 x^{3} + 27 x^{2} + 9 x + 1^{3}$

Step 3.10

One to any power is one.

$27 x^{3} + 27 x^{2} + 9 x + 1$