Algebra Examples

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

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the product rule to $2 x$ .

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

Step 1.2.2

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

$8 x^{3} + 3 {(2 x)}^{2} \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Step 1.2.3

Apply the product rule to $2 x$ .

$8 x^{3} + 3 (2^{2} x^{2}) \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Step 1.2.4

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

$8 x^{3} + 3 (4 x^{2}) \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Step 1.2.5

Multiply $4$ by $3$ .

$8 x^{3} + 12 x^{2} \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Step 1.2.6

Multiply $3$ by $12$ .

$8 x^{3} + 36 x^{2} + 3 (2 x) \cdot 3^{2} + 3^{3}$

Step 1.2.7

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

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Step 1.2.7.1

Move $3^{2}$ .

$8 x^{3} + 36 x^{2} + 3^{2} \cdot 3 (2 x) + 3^{3}$

Step 1.2.7.2

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

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Step 1.2.7.2.1

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

$8 x^{3} + 36 x^{2} + 3^{2} \cdot 3^{1} (2 x) + 3^{3}$

Step 1.2.7.2.2

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

$8 x^{3} + 36 x^{2} + 3^{2 + 1} (2 x) + 3^{3}$

Step 1.2.7.3

Add $2$ and $1$ .

$8 x^{3} + 36 x^{2} + 3^{3} (2 x) + 3^{3}$

Step 1.2.8

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

$8 x^{3} + 36 x^{2} + 27 (2 x) + 3^{3}$

Step 1.2.9

Multiply $2$ by $27$ .

$8 x^{3} + 36 x^{2} + 54 x + 3^{3}$

Step 1.2.10

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

$8 x^{3} + 36 x^{2} + 54 x + 27$

Step 2

The leading term in a polynomial is the term with the highest degree.

$8 x^{3}$

Step 3

The leading coefficient in a polynomial is the coefficient of the leading term.

$8$