What is factor 4x^4+8x^2y^2+9y^4 ?

The solution to factor 4x^4+8x^2y^2+9y^4 is (2x^2+3y^2+2xy)(2x^2+3y^2-2xy)

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factor 4x^4+8x^2y^2+9y^4

factor

4 x^{4} + 8 x^{2} y^{2} + 9 y^{4}

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

Solution steps

4 x^{4} + 8 x^{2} y^{2} + 9 y^{4}

Add and subtract

4 x^{2} y^{2}

= 4 x^{4} + 12 x^{2} y^{2} + 9 y^{4} - 4 x^{2} y^{2}

Factor

4 x^{4} + 12 x^{2} y^{2} + 9 y^{4} : (2 x^{2} + 3 y^{2})^{2}

= (2 x^{2} + 3 y^{2})^{2} - 4 x^{2} y^{2}

Apply exponent rules

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

Factor

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

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

\frac{5}{6 x} - \frac{4}{9 x}

(5^{3})^{3}

(4 x - 9) (2 x^{2} + 2 x + 1)

(a + 2 b)^{3}

20 a b^{2} - 5 a^{3} b

What is factor 4x^4+8x^2y^2+9y^4 ?
The solution to factor 4x^4+8x^2y^2+9y^4 is (2x^2+3y^2+2xy)(2x^2+3y^2-2xy)