What is factor a^8+8a^4b^4+16b^8 ?

The solution to factor a^8+8a^4b^4+16b^8 is (a^4+4b^4)^2

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factor a^8+8a^4b^4+16b^8

factor

a^{8} + 8 a^{4} b^{4} + 16 b^{8}

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

Solution steps

a^{8} + 8 a^{4} b^{4} + 16 b^{8}

Break the expression into groups

= (a^{8} + 4 a^{4} b^{4}) + (4 a^{4} b^{4} + 16 b^{8})

Factor out

a^{4}

from

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

Factor out

4 b^{4}

from

4 a^{4} b^{4} + 16 b^{8} : 4 b^{4} (a^{4} + 4 b^{4})

= a^{4} (a^{4} + 4 b^{4}) + 4 b^{4} (a^{4} + 4 b^{4})

Factor out common term

a^{4} + 4 b^{4}

= (a^{4} + 4 b^{4}) (a^{4} + 4 b^{4})

Apply exponent rule:

aa = a^{2}

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

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

2 - \frac{2}{3}

42

\frac{3}{4} + \frac{1}{10}

(y - 1)^{2} - 13 (y - 1) + 36 = 0

2 (x - 1) \geq 8

What is factor a^8+8a^4b^4+16b^8 ?
The solution to factor a^8+8a^4b^4+16b^8 is (a^4+4b^4)^2