What is (a^6-b^6)/(a-b) ?

The solution to (a^6-b^6)/(a-b) is (a+b)(a^2-ab+b^2)(a^2+ab+b^2)

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simplify (a^6-b^6)/(a-b)

simplify

\frac{a ^{6} - b ^{6}}{a - b}

(a + b) (a^{2} - ab + b^{2}) (a^{2} + ab + b^{2})

Solution steps

\frac{a ^{6} - b ^{6}}{a - b}

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Apply Sum of Cubes Formula:

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

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

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

Apply Difference of Cubes Formula:

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

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

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

Cancel the common factor:

a - b

= (a + b) (a^{2} - ab + b^{2}) (a^{2} + ab + b^{2})

\frac{- 26 a ^{5} b ^{6}}{- 13 b ^{3}}

- 63

5 x (3 x + 2) - 4 (3 x + 2)

0^{2}

\frac{3}{7 x y} + \frac{2}{5}

What is (a^6-b^6)/(a-b) ?
The solution to (a^6-b^6)/(a-b) is (a+b)(a^2-ab+b^2)(a^2+ab+b^2)