What is (x^6-y^6)/(x+y) ?

The solution to (x^6-y^6)/(x+y) is (x^2-xy+y^2)(x-y)(x^2+xy+y^2)

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simplify (x^6-y^6)/(x+y)

simplify

\frac{x ^{6} - y ^{6}}{x + y}

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

Solution steps

\frac{x ^{6} - y ^{6}}{x + y}

x^{6} = (x^{3})^{2}

y^{6} = (y^{3})^{2}

= \frac{( x ^{3} ) ^{2} - ( y ^{3} ) ^{2}}{x + y}

Apply Difference of Two Squares Formula:

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

(x^{3})^{2} - (y^{3})^{2} = (x^{3} + y^{3}) (x^{3} - y^{3})

= \frac{( x ^{3} + y ^{3} ) ( x ^{3} - y ^{3} )}{x + y}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

= \frac{( x + y ) ( x ^{2} - x y + y ^{2} ) ( x ^{3} - y ^{3} )}{x + y}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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

Cancel the common factor:

x + y

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

4 - \frac{7}{2}

(\frac{5}{4} - s)^{2}

(a + b - c) (a - b + c)

- 5.5 3

- 5 \cdot 5

What is (x^6-y^6)/(x+y) ?
The solution to (x^6-y^6)/(x+y) is (x^2-xy+y^2)(x-y)(x^2+xy+y^2)