Pre-Algebra Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

One to any power is one.

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

Step 2.2

One to any power is one.

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

Step 2.3

Multiply $3$ by $1$ .

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

Step 2.4

Multiply $- 1$ by $3$ .

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

Step 2.5

Multiply $3$ by $1$ .

$1 - 3 x + 3 {(- x)}^{2} + {(- x)}^{3}$

Step 2.6

Apply the product rule to $- x$ .

$1 - 3 x + 3 ({(- 1)}^{2} x^{2}) + {(- x)}^{3}$

Step 2.7

Raise $- 1$ to the power of $2$ .

$1 - 3 x + 3 (1 x^{2}) + {(- x)}^{3}$

Step 2.8

Multiply $x^{2}$ by $1$ .

$1 - 3 x + 3 x^{2} + {(- x)}^{3}$

Step 2.9

Apply the product rule to $- x$ .

$1 - 3 x + 3 x^{2} + {(- 1)}^{3} x^{3}$

Step 2.10

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

$1 - 3 x + 3 x^{2} - x^{3}$