What is factor 4a^4+8a^2b^2+9b^4 ?

The solution to factor 4a^4+8a^2b^2+9b^4 is (2a^2+3b^2+2ab)(2a^2+3b^2-2ab)

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factor 4a^4+8a^2b^2+9b^4

factor

4 a^{4} + 8 a^{2} b^{2} + 9 b^{4}

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

Solution steps

4 a^{4} + 8 a^{2} b^{2} + 9 b^{4}

Add and subtract

4 a^{2} b^{2}

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

Apply exponent rules

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

Factor

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

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

a^{2} + b^{2} - 2 b^{2} - 3 a^{2} - a^{2} + b^{2}

7^{l o g_{7} (8)}

a^{2 n} b^{4 n} - \frac{1}{25}

\frac{6 x ^{2} + 5 x - 6}{15 x ^{2} - 7 x - 2}

30 \cdot 2

What is factor 4a^4+8a^2b^2+9b^4 ?
The solution to factor 4a^4+8a^2b^2+9b^4 is (2a^2+3b^2+2ab)(2a^2+3b^2-2ab)