Trigonometry Examples

${(x + 2)}^{6}$

Step 1

Use the Binomial Theorem.

$x^{6} + 6 x^{5} \cdot 2 + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $6$ .

$x^{6} + 12 x^{5} + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.2

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

$x^{6} + 12 x^{5} + 15 x^{4} \cdot 4 + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.3

Multiply $4$ by $15$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.4

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

$x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 8 + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.5

Multiply $8$ by $20$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.6

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

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 16 + 6 x \cdot 2^{5} + 2^{6}$

Step 2.7

Multiply $16$ by $15$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 2^{5} + 2^{6}$

Step 2.8

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

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 32 + 2^{6}$

Step 2.9

Multiply $32$ by $6$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 2^{6}$

Step 2.10

Raise $2$ to the power of $6$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 64$