What is factor a^4+2a^2b^2+b^4 ?

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

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factor a^4+2a^2b^2+b^4

factor

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

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

Solution steps

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

Break the expression into groups

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

Factor out

a^{2}

from

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

Factor out

b^{2}

from

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

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

Factor out common term

a^{2} + b^{2}

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

Apply exponent rule:

aa = a^{2}

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

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

\frac{9 x - 1}{13} - \frac{5 x - 8}{4} = x + 6

3 x^{2} + 3 x - 1 = 0

x + 3 \leq 2 x - 7

\frac{3 x + 2}{5} + \frac{3 - 6 x}{10} = \frac{1 - x}{2}

x^{9}

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