What is factor a^8-4a^4b^4+4b^8 ?

The solution to factor a^8-4a^4b^4+4b^8 is (a^4-2b^4)^2

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factor a^8-4a^4b^4+4b^8

factor

a^{8} - 4 a^{4} b^{4} + 4 b^{8}

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

Solution steps

a^{8} - 4 a^{4} b^{4} + 4 b^{8}

Break the expression into groups

= (a^{8} - 2 a^{4} b^{4}) + (- 2 a^{4} b^{4} + 4 b^{8})

Factor out

a^{4}

from

a^{8} - 2 a^{4} b^{4} : a^{4} (a^{4} - 2 b^{4})

Factor out

- 2 b^{4}

from

- 2 a^{4} b^{4} + 4 b^{8} : - 2 b^{4} (a^{4} - 2 b^{4})

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

Factor out common term

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

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

Apply exponent rule:

aa = a^{2}

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

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

- 16 + - 25

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\frac{( \frac{3}{4} + \frac{7}{8} )}{( \frac{2}{5} - \frac{8}{9} )}

\frac{sec ( θ )}{tan ( θ )}

(1 - sin (x)) (1 + sin (x))

What is factor a^8-4a^4b^4+4b^8 ?
The solution to factor a^8-4a^4b^4+4b^8 is (a^4-2b^4)^2