What is (m^6-n^6)/(m^2-n^2) ?

The solution to (m^6-n^6)/(m^2-n^2) is (m^2-mn+n^2)(m^2+mn+n^2)

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simplify (m^6-n^6)/(m^2-n^2)

simplify

\frac{m ^{6} - n ^{6}}{m ^{2} - n ^{2}}

(m^{2} - mn + n^{2}) (m^{2} + mn + n^{2})

Solution steps

\frac{m ^{6} - n ^{6}}{m ^{2} - n ^{2}}

Factor

m^{6} - n^{6} : (m + n) (m^{2} - mn + n^{2}) (m - n) (m^{2} + mn + n^{2})

= \frac{( m + n ) ( m ^{2} - mn + n ^{2} ) ( m - n ) ( m ^{2} + mn + n ^{2} )}{m ^{2} - n ^{2}}

Apply Difference of Two Squares Formula:

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

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

= \frac{( m + n ) ( m ^{2} - mn + n ^{2} ) ( m - n ) ( m ^{2} + mn + n ^{2} )}{( m + n ) ( m - n )}

Cancel the common factor:

m + n

= \frac{( m ^{2} - mn + n ^{2} ) ( m - n ) ( m ^{2} + mn + n ^{2} )}{m - n}

Cancel the common factor:

m - n

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

\frac{1}{3} (3 x^{2} + 9)^{2} - 9

\frac{3}{x} \cdot \frac{x - 1}{6}

\frac{x}{2}

\frac{2 x ^{2} - 12 x}{x ^{2} - 3 x - 18}

\frac{3}{8} \times \frac{5}{6} \div \frac{1}{4}

What is (m^6-n^6)/(m^2-n^2) ?
The solution to (m^6-n^6)/(m^2-n^2) is (m^2-mn+n^2)(m^2+mn+n^2)