Pre-Algebra Examples

${(x - 4)}^{4}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $- 4$ by $4$ .

$x^{4} - 16 x^{3} + 6 x^{2} {(- 4)}^{2} + 4 x {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.2

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

$x^{4} - 16 x^{3} + 6 x^{2} \cdot 16 + 4 x {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.3

Multiply $16$ by $6$ .

$x^{4} - 16 x^{3} + 96 x^{2} + 4 x {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.4

Raise $- 4$ to the power of $3$ .

$x^{4} - 16 x^{3} + 96 x^{2} + 4 x \cdot - 64 + {(- 4)}^{4}$

Step 2.5

Multiply $- 64$ by $4$ .

$x^{4} - 16 x^{3} + 96 x^{2} - 256 x + {(- 4)}^{4}$

Step 2.6

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

$x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256$