Solve E=(m+n)(m-n)(m^{2}+n^{2})(m^4+n^4)+n^8-m^8+1

$$E = ( m + n ) ( m - n ) ( m ^ { 2 } + n ^ { 2 } ) ( m ^ { 4 } + n ^ { 4 } ) + n ^ { 8 } - m ^ { 8 } + 1$$

Solve for E

$$E=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+n by m-n and combine like terms.

$$E=\left(m^{2}-n^{2}\right)\left(m^{2}+n^{2}\right)\left(m^{4}+n^{4}\right)+n^{8}-m^{8}+1$$

Use the distributive property to multiply m^{2}-n^{2} by m^{2}+n^{2} and combine like terms.

$$E=\left(m^{4}-n^{4}\right)\left(m^{4}+n^{4}\right)+n^{8}-m^{8}+1$$

Consider \left(m^{4}-n^{4}\right)\left(m^{4}+n^{4}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$E=\left(m^{4}\right)^{2}-\left(n^{4}\right)^{2}+n^{8}-m^{8}+1$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$E=m^{8}-\left(n^{4}\right)^{2}+n^{8}-m^{8}+1$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$E=m^{8}-n^{8}+n^{8}-m^{8}+1$$

Combine -n^{8} and n^{8} to get 0.

$$E=m^{8}-m^{8}+1$$

Combine m^{8} and -m^{8} to get 0.

$$E=1$$

Solve for m (complex solution)

$$m\in \mathrm{C}$$

$$E=1$$

Solve for m

$$m\in \mathrm{R}$$

$$E=1$$