What is factor 16a^4+8a^2b^2+9b^4 ?

The solution to factor 16a^4+8a^2b^2+9b^4 is (4a^2+3b^2+4ab)(4a^2+3b^2-4ab)

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factor 16a^4+8a^2b^2+9b^4

factor

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

(4 a^{2} + 3 b^{2} + 4 ab) (4 a^{2} + 3 b^{2} - 4 ab)

Solution steps

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

Add and subtract

16 a^{2} b^{2}

= 16 a^{4} + 24 a^{2} b^{2} + 9 b^{4} - 16 a^{2} b^{2}

Factor

16 a^{4} + 24 a^{2} b^{2} + 9 b^{4} : (4 a^{2} + 3 b^{2})^{2}

= (4 a^{2} + 3 b^{2})^{2} - 16 a^{2} b^{2}

Apply exponent rules

= (4 a^{2} + 3 b^{2})^{2} - (4 ab)^{2}

Factor

(4 a^{2} + 3 b^{2})^{2} - (4 ab)^{2} : (4 a^{2} + 3 b^{2} + 4 ab) (4 a^{2} + 3 b^{2} - 4 ab)

= (4 a^{2} + 3 b^{2} + 4 ab) (4 a^{2} + 3 b^{2} - 4 ab)

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

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

\frac{( x - 1 )}{( x ^{3} - 1 )}

(2 x^{2} \cdot y)^{4}

- 4 a \cdot (a^{- 1} \cdot b^{2})^{3}

What is factor 16a^4+8a^2b^2+9b^4 ?
The solution to factor 16a^4+8a^2b^2+9b^4 is (4a^2+3b^2+4ab)(4a^2+3b^2-4ab)