Expand the Trigonometric Expression (x+4)^8

${(x + 4)}^{8}$

Step 1

Use the Binomial Theorem.

$x^{8} + 8 x^{7} \cdot 4 + 28 x^{6} \cdot 4^{2} + 56 x^{5} \cdot 4^{3} + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Step 2

Simplify each term.

Multiply $4$ by $8$ .

$x^{8} + 32 x^{7} + 28 x^{6} \cdot 4^{2} + 56 x^{5} \cdot 4^{3} + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

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

$x^{8} + 32 x^{7} + 28 x^{6} \cdot 16 + 56 x^{5} \cdot 4^{3} + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Multiply $16$ by $28$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 56 x^{5} \cdot 4^{3} + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

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

$x^{8} + 32 x^{7} + 448 x^{6} + 56 x^{5} \cdot 64 + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Multiply $64$ by $56$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 70 x^{4} \cdot 4^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

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

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 70 x^{4} \cdot 256 + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Multiply $256$ by $70$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 56 x^{3} \cdot 4^{5} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Raise $4$ to the power of $5$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 56 x^{3} \cdot 1024 + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Multiply $1024$ by $56$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 28 x^{2} \cdot 4^{6} + 8 x \cdot 4^{7} + 4^{8}$

Raise $4$ to the power of $6$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 28 x^{2} \cdot 4096 + 8 x \cdot 4^{7} + 4^{8}$

Multiply $4096$ by $28$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 114688 x^{2} + 8 x \cdot 4^{7} + 4^{8}$

Raise $4$ to the power of $7$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 114688 x^{2} + 8 x \cdot 16384 + 4^{8}$

Multiply $16384$ by $8$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 114688 x^{2} + 131072 x + 4^{8}$

Raise $4$ to the power of $8$ .

$x^{8} + 32 x^{7} + 448 x^{6} + 3584 x^{5} + 17920 x^{4} + 57344 x^{3} + 114688 x^{2} + 131072 x + 65536$

Expand the Trigonometric Expression (x+4)^8

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