Algebra Examples

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

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.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $2$ by $3$ .

$x^{3} + 6 x^{2} + 3 x \cdot 2^{2} + 2^{3}$

Step 1.2.2

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

$x^{3} + 6 x^{2} + 3 x \cdot 4 + 2^{3}$

Step 1.2.3

Multiply $4$ by $3$ .

$x^{3} + 6 x^{2} + 12 x + 2^{3}$

Step 1.2.4

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

$x^{3} + 6 x^{2} + 12 x + 8$

Step 2

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

$x^{3}$

Step 3

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

$1$