Precalculus Examples

${(x - 10)}^{5}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $- 10$ by $5$ .

$x^{5} - 50 x^{4} + 10 x^{3} {(- 10)}^{2} + 10 x^{2} {(- 10)}^{3} + 5 x {(- 10)}^{4} + {(- 10)}^{5}$

Step 2.2

Raise $- 10$ to the power of $2$ .

$x^{5} - 50 x^{4} + 10 x^{3} \cdot 100 + 10 x^{2} {(- 10)}^{3} + 5 x {(- 10)}^{4} + {(- 10)}^{5}$

Step 2.3

Multiply $100$ by $10$ .

$x^{5} - 50 x^{4} + 1000 x^{3} + 10 x^{2} {(- 10)}^{3} + 5 x {(- 10)}^{4} + {(- 10)}^{5}$

Step 2.4

Raise $- 10$ to the power of $3$ .

$x^{5} - 50 x^{4} + 1000 x^{3} + 10 x^{2} \cdot - 1000 + 5 x {(- 10)}^{4} + {(- 10)}^{5}$

Step 2.5

Multiply $- 1000$ by $10$ .

$x^{5} - 50 x^{4} + 1000 x^{3} - 10000 x^{2} + 5 x {(- 10)}^{4} + {(- 10)}^{5}$

Step 2.6

Raise $- 10$ to the power of $4$ .

$x^{5} - 50 x^{4} + 1000 x^{3} - 10000 x^{2} + 5 x \cdot 10000 + {(- 10)}^{5}$

Step 2.7

Multiply $10000$ by $5$ .

$x^{5} - 50 x^{4} + 1000 x^{3} - 10000 x^{2} + 50000 x + {(- 10)}^{5}$

Step 2.8

Raise $- 10$ to the power of $5$ .

$x^{5} - 50 x^{4} + 1000 x^{3} - 10000 x^{2} + 50000 x - 100000$