Algebra Examples

${(2 + x)}^{5}$

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.

$2^{5} + 5 \cdot 2^{4} x + 10 \cdot 2^{3} x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2

Simplify terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Raise $2$ to the power of $5$ .

$32 + 5 \cdot 2^{4} x + 10 \cdot 2^{3} x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.2

Raise $2$ to the power of $4$ .

$32 + 5 \cdot 16 x + 10 \cdot 2^{3} x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.3

Multiply $5$ by $16$ .

$32 + 80 x + 10 \cdot 2^{3} x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.4

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

$32 + 80 x + 10 \cdot 8 x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.5

Multiply $10$ by $8$ .

$32 + 80 x + 80 x^{2} + 10 \cdot 2^{2} x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.6

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

$32 + 80 x + 80 x^{2} + 10 \cdot 4 x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.7

Multiply $10$ by $4$ .

$32 + 80 x + 80 x^{2} + 40 x^{3} + 5 \cdot 2 x^{4} + x^{5}$

Step 1.2.1.8

Multiply $5$ by $2$ .

$32 + 80 x + 80 x^{2} + 40 x^{3} + 10 x^{4} + x^{5}$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Move $32$ .

$80 x + 80 x^{2} + 40 x^{3} + 10 x^{4} + x^{5} + 32$

Step 1.2.2.2

Move $80 x$ .

$80 x^{2} + 40 x^{3} + 10 x^{4} + x^{5} + 80 x + 32$

Step 1.2.2.3

Move $80 x^{2}$ .

$40 x^{3} + 10 x^{4} + x^{5} + 80 x^{2} + 80 x + 32$

Step 1.2.2.4

Move $40 x^{3}$ .

$10 x^{4} + x^{5} + 40 x^{3} + 80 x^{2} + 80 x + 32$

Step 1.2.2.5

Reorder $10 x^{4}$ and $x^{5}$ .

$x^{5} + 10 x^{4} + 40 x^{3} + 80 x^{2} + 80 x + 32$

Step 2

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

$x^{5}$

Step 3

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

$1$