What is (m^5+n^5)/(m+n) ?

The solution to (m^5+n^5)/(m+n) is m^4-m^3n+m^2n^2-mn^3+n^4

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simplify (m^5+n^5)/(m+n)

simplify

\frac{m ^{5} + n ^{5}}{m + n}

m^{4} - m^{3} n + m^{2} n^{2} - m n^{3} + n^{4}

Solution steps

\frac{m ^{5} + n ^{5}}{m + n}

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

m^{5} + n^{5} = (m + n) (m^{4} - m^{3} n + m^{2} n^{2} - m n^{3} + n^{4})

= \frac{( m + n ) ( m ^{4} - m ^{3} n + m ^{2} n ^{2} - m n ^{3} + n ^{4} )}{m + n}

Cancel the common factor:

m + n

= m^{4} - m^{3} n + m^{2} n^{2} - m n^{3} + n^{4}

- b^{4} + 1

(5 - 9 a^{3}) + (4 a^{2} + 6 a - 3)

5 (2 x)

7 (x - 2) + 10 (- 5 x + 6)

- 7^{5}

What is (m^5+n^5)/(m+n) ?
The solution to (m^5+n^5)/(m+n) is m^4-m^3n+m^2n^2-mn^3+n^4