What is factor 4a^4+3a^2b^2+9b^4 ?

The solution to factor 4a^4+3a^2b^2+9b^4 is (2a^2+3b^2+3ab)(2a^2+3b^2-3ab)

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factor 4a^4+3a^2b^2+9b^4

factor

4 a^{4} + 3 a^{2} b^{2} + 9 b^{4}

(2 a^{2} + 3 b^{2} + 3 ab) (2 a^{2} + 3 b^{2} - 3 ab)

Solution steps

4 a^{4} + 3 a^{2} b^{2} + 9 b^{4}

Add and subtract

9 a^{2} b^{2}

= 4 a^{4} + 12 a^{2} b^{2} + 9 b^{4} - 9 a^{2} b^{2}

Factor

4 a^{4} + 12 a^{2} b^{2} + 9 b^{4} : (2 a^{2} + 3 b^{2})^{2}

= (2 a^{2} + 3 b^{2})^{2} - 9 a^{2} b^{2}

Apply exponent rules

= (2 a^{2} + 3 b^{2})^{2} - (3 ab)^{2}

Factor

(2 a^{2} + 3 b^{2})^{2} - (3 ab)^{2} : (2 a^{2} + 3 b^{2} + 3 ab) (2 a^{2} + 3 b^{2} - 3 ab)

= (2 a^{2} + 3 b^{2} + 3 ab) (2 a^{2} + 3 b^{2} - 3 ab)

\frac{2 x - 1}{x + 3} - \frac{x + 1}{x - 3}

125 + 64 n^{3}

10 a^{2} - 5 a + 15 a^{3}

- 1 \frac{7}{8} \cdot (- \frac{2}{5})

x (x - 2) (x + 2)

What is factor 4a^4+3a^2b^2+9b^4 ?
The solution to factor 4a^4+3a^2b^2+9b^4 is (2a^2+3b^2+3ab)(2a^2+3b^2-3ab)