Solve 3(x^2+1)(x^4+1)(x^8+1)(x^16+1)+1

$$3 ( x ^ { 2 } + 1 ) ( x ^ { 4 } + 1 ) ( x ^ { 8 } + 1 ) ( x ^ { 16 } + 1 ) + 1$$

Expand

$$3x^{30}+3x^{28}+3x^{26}+3x^{24}+3x^{22}+3x^{20}+3x^{18}+3x^{16}+3x^{14}+3x^{12}+3x^{10}+3x^{8}+3x^{6}+3x^{4}+3x^{2}+4$$

Solution Steps

Use the distributive property to multiply 3 by x^{2}+1.

$$\left(3x^{2}+3\right)\left(x^{4}+1\right)\left(x^{8}+1\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{2}+3 by x^{4}+1.

$$\left(3x^{6}+3x^{2}+3x^{4}+3\right)\left(x^{8}+1\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{6}+3x^{2}+3x^{4}+3 by x^{8}+1.

$$\left(3x^{14}+3x^{6}+3x^{10}+3x^{2}+3x^{12}+3x^{4}+3x^{8}+3\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{14}+3x^{6}+3x^{10}+3x^{2}+3x^{12}+3x^{4}+3x^{8}+3 by x^{16}+1.

$$3x^{30}+3x^{14}+3x^{22}+3x^{6}+3x^{26}+3x^{10}+3x^{18}+3x^{2}+3x^{28}+3x^{12}+3x^{20}+3x^{4}+3x^{24}+3x^{8}+3x^{16}+3+1$$

Add 3 and 1 to get 4.

$$3x^{30}+3x^{14}+3x^{22}+3x^{6}+3x^{26}+3x^{10}+3x^{18}+3x^{2}+3x^{28}+3x^{12}+3x^{20}+3x^{4}+3x^{24}+3x^{8}+3x^{16}+4$$

Evaluate

$$3\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)\left(x^{16}+1\right)+1$$

Solution Steps

Use the distributive property to multiply 3 by x^{2}+1.

$$\left(3x^{2}+3\right)\left(x^{4}+1\right)\left(x^{8}+1\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{2}+3 by x^{4}+1.

$$\left(3x^{6}+3x^{2}+3x^{4}+3\right)\left(x^{8}+1\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{6}+3x^{2}+3x^{4}+3 by x^{8}+1.

$$\left(3x^{14}+3x^{6}+3x^{10}+3x^{2}+3x^{12}+3x^{4}+3x^{8}+3\right)\left(x^{16}+1\right)+1$$

Use the distributive property to multiply 3x^{14}+3x^{6}+3x^{10}+3x^{2}+3x^{12}+3x^{4}+3x^{8}+3 by x^{16}+1.

$$3x^{30}+3x^{14}+3x^{22}+3x^{6}+3x^{26}+3x^{10}+3x^{18}+3x^{2}+3x^{28}+3x^{12}+3x^{20}+3x^{4}+3x^{24}+3x^{8}+3x^{16}+3+1$$

Add 3 and 1 to get 4.

$$3x^{30}+3x^{14}+3x^{22}+3x^{6}+3x^{26}+3x^{10}+3x^{18}+3x^{2}+3x^{28}+3x^{12}+3x^{20}+3x^{4}+3x^{24}+3x^{8}+3x^{16}+4$$