Expand the Trigonometric Expression (y+2)^6

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $2$ by $6$ .

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

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

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

Multiply $4$ by $15$ .

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

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

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

Multiply $8$ by $20$ .

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

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

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

Multiply $16$ by $15$ .

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

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

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

Multiply $32$ by $6$ .

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

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

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