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

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

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

factor

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

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

Solution steps

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

Add and subtract

a^{2} b^{2}

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

Factor

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

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

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

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

Factor

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

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

x^{4} - 3 x - 2

15 x^{3} + 3 x^{2} y

(r + 2)^{3}

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

2 x^{2} y^{2} + 3 x y - 4 y^{3}

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