What is factor a^4-2a^3*b+a^2*b^2-b^4 ?

The solution to factor a^4-2a^3*b+a^2*b^2-b^4 is (a^2-ab+b^2)(a^2-ab-b^2)

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factor a^4-2a^3b+a^2b^2-b^4

factor

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

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

Solution steps

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

Factor

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

= a^{2} (a - b)^{2} - b^{4}

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

b^{4} = (b^{2})^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Simplify

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

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

5^{2} n - 3 - 5^{2} n - 1 + 2 5^{n} - 1

f^{- 4}

36 a^{2} - 12 a + 1 - 25 b^{2}

\frac{( ( 6 y ^{3} ) ^{4} )}{( 2 y ^{5} )}

\frac{( 1 + sin ( x ) )}{n}

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