What is ((m^4-n^4))/((m+n)) ?

The solution to ((m^4-n^4))/((m+n)) is (m^2+n^2)(m-n)

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simplify ((m^4-n^4))/((m+n))

simplify

\frac{( m ^{4} - n ^{4} )}{( m + n )}

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

Solution steps

\frac{m ^{4} - n ^{4}}{m + n}

m^{4} = (m^{2})^{2}

n^{4} = (n^{2})^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

m + n

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

2 7^{3}

2 \frac{4}{3}

\frac{32}{2 3}

3 (5 x + 9 - 4 x)

11 x + 9 y - 8 w + 4 y - 7 x + 7 w

What is ((m^4-n^4))/((m+n)) ?
The solution to ((m^4-n^4))/((m+n)) is (m^2+n^2)(m-n)