Solve (2+1)(2^2+1)(2^4+1)+(2^7-1)^2

$$( 2 + 1 ) ( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) + ( 2 ^ { 7 } - 1 ) ^ { 2 }$$

Evaluate

$$16384$$

Solution Steps

Add 2 and 1 to get 3.

$$3\left(2^{2}+1\right)\left(2^{4}+1\right)+\left(2^{7}-1\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$3\left(4+1\right)\left(2^{4}+1\right)+\left(2^{7}-1\right)^{2}$$

Add 4 and 1 to get 5.

$$3\times 5\left(2^{4}+1\right)+\left(2^{7}-1\right)^{2}$$

Multiply 3 and 5 to get 15.

$$15\left(2^{4}+1\right)+\left(2^{7}-1\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$15\left(16+1\right)+\left(2^{7}-1\right)^{2}$$

Add 16 and 1 to get 17.

$$15\times 17+\left(2^{7}-1\right)^{2}$$

Multiply 15 and 17 to get 255.

$$255+\left(2^{7}-1\right)^{2}$$

Calculate 2 to the power of 7 and get 128.

$$255+\left(128-1\right)^{2}$$

Subtract 1 from 128 to get 127.

$$255+127^{2}$$

Calculate 127 to the power of 2 and get 16129.

$$255+16129$$

Add 255 and 16129 to get 16384.

$$16384$$

Factor

$$2^{14}$$