What is factor m^{16}-n^{16} ?

The solution to factor m^{16}-n^{16} is (m^8+n^8)(m^4+n^4)(m^2+n^2)(m+n)(m-n)

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factor m^{16}-n^{16}

factor

m^{16} - n^{16}

(m^{8} + n^{8}) (m^{4} + n^{4}) (m^{2} + n^{2}) (m + n) (m - n)

Solution steps

m^{16} - n^{16}

m^{16} = (m^{8})^{2}

n^{16} = (n^{8})^{2}

= (m^{8})^{2} - (n^{8})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(m^{8})^{2} - (n^{8})^{2} = (m^{8} + n^{8}) (m^{8} - n^{8})

= (m^{8} + n^{8}) (m^{8} - n^{8})

Factor

m^{8} - n^{8} : (m^{4} + n^{4}) (m^{2} + n^{2}) (m + n) (m - n)

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

(x - y)^{2} - x^{2} + y^{2}

\frac{( x + 15 )}{( x ^{2} - 9 )} + \frac{2}{( x + 3 )}

(a^{6})^{2}

\frac{4 + 2 \cdot ( 1 + 8 x ^{9} ) - 7 + 12}{4}

\frac{( cos ^{2} ( t ) - 1 )}{2}

What is factor m^{16}-n^{16} ?
The solution to factor m^{16}-n^{16} is (m^8+n^8)(m^4+n^4)(m^2+n^2)(m+n)(m-n)