What is factor x^4+7x^2y^2+16y^4 ?

The solution to factor x^4+7x^2y^2+16y^4 is (x^2+4y^2+xy)(x^2+4y^2-xy)

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factor x^4+7x^2y^2+16y^4

factor

x^{4} + 7 x^{2} y^{2} + 16 y^{4}

(x^{2} + 4 y^{2} + x y) (x^{2} + 4 y^{2} - x y)

Solution steps

x^{4} + 7 x^{2} y^{2} + 16 y^{4}

Add and subtract

x^{2} y^{2}

= x^{4} + 8 x^{2} y^{2} + 16 y^{4} - x^{2} y^{2}

Factor

x^{4} + 8 x^{2} y^{2} + 16 y^{4} : (x^{2} + 4 y^{2})^{2}

= (x^{2} + 4 y^{2})^{2} - x^{2} y^{2}

Apply exponent rule:

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

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

= (x^{2} + 4 y^{2})^{2} - (x y)^{2}

Factor

(x^{2} + 4 y^{2})^{2} - (x y)^{2} : (x^{2} + 4 y^{2} + x y) (x^{2} + 4 y^{2} - x y)

= (x^{2} + 4 y^{2} + x y) (x^{2} + 4 y^{2} - x y)

\frac{1}{x ^{- 1} \cdot x}

(5 x - 4)^{3}

15 x^{2} x^{2} - 8 x^{4}

(x^{2} - 2 y)^{3}

(x^{5} + 4 x)^{3}

What is factor x^4+7x^2y^2+16y^4 ?
The solution to factor x^4+7x^2y^2+16y^4 is (x^2+4y^2+xy)(x^2+4y^2-xy)