What is (a^5+b^5)/(a+b) ?

The solution to (a^5+b^5)/(a+b) is a^4-a^3b+a^2b^2-ab^3+b^4

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simplify (a^5+b^5)/(a+b)

simplify

\frac{a ^{5} + b ^{5}}{a + b}

a^{4} - a^{3} b + a^{2} b^{2} - a b^{3} + b^{4}

Solution steps

\frac{a ^{5} + b ^{5}}{a + b}

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

a^{5} + b^{5} = (a + b) (a^{4} - a^{3} b + a^{2} b^{2} - a b^{3} + b^{4})

= \frac{( a + b ) ( a ^{4} - a ^{3} b + a ^{2} b ^{2} - a b ^{3} + b ^{4} )}{a + b}

Cancel the common factor:

a + b

= a^{4} - a^{3} b + a^{2} b^{2} - a b^{3} + b^{4}

(4 x^{2} + 3 x + 2) + (7 x^{2} + 7 x + 3)

(1) - 2

0.5 \cdot 0.5 \cdot 0.5

(x + 5) (2 - x)

\frac{1}{3} + \frac{2}{9} + \frac{1}{27} + \frac{2}{81} + \frac{1}{243} + \frac{2}{729}

What is (a^5+b^5)/(a+b) ?
The solution to (a^5+b^5)/(a+b) is a^4-a^3b+a^2b^2-ab^3+b^4