What is factor a^5-a^3b^2-a^2b^3+b^5 ?

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

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factor a^5-a^3b^2-a^2b^3+b^5

factor

a^{5} - a^{3} b^{2} - a^{2} b^{3} + b^{5}

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

Solution steps

a^{5} - a^{3} b^{2} - a^{2} b^{3} + b^{5}

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

Factor out

a^{3}

from

a^{5} - a^{3} b^{2} : a^{3} (a^{2} - b^{2})

Factor out

b^{3}

from

b^{5} - a^{2} b^{3} : b^{3} (b^{2} - a^{2})

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

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

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

Factor out common term

a^{2} - b^{2}

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

Factor

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

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

\frac{3}{4} - \frac{1}{5}

- x^{2} + 8 x - 7

x^{2} + 3 x < 4

7 b^{2} - 13 b = 10 - 4 b

- x - 3 = 2 x - 6

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