What is factor a^4+a^2b^2+25b^4 ?

The solution to factor a^4+a^2b^2+25b^4 is (a^2+5b^2+3ab)(a^2+5b^2-3ab)

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factor a^4+a^2b^2+25b^4

factor

a^{4} + a^{2} b^{2} + 25 b^{4}

(a^{2} + 5 b^{2} + 3 ab) (a^{2} + 5 b^{2} - 3 ab)

Solution steps

a^{4} + a^{2} b^{2} + 25 b^{4}

Add and subtract

9 a^{2} b^{2}

= a^{4} + 10 a^{2} b^{2} + 25 b^{4} - 9 a^{2} b^{2}

Factor

a^{4} + 10 a^{2} b^{2} + 25 b^{4} : (a^{2} + 5 b^{2})^{2}

= (a^{2} + 5 b^{2})^{2} - 9 a^{2} b^{2}

Apply exponent rules

= (a^{2} + 5 b^{2})^{2} - (3 ab)^{2}

Factor

(a^{2} + 5 b^{2})^{2} - (3 ab)^{2} : (a^{2} + 5 b^{2} + 3 ab) (a^{2} + 5 b^{2} - 3 ab)

= (a^{2} + 5 b^{2} + 3 ab) (a^{2} + 5 b^{2} - 3 ab)

\frac{( 3 ^{n} \cdot 9 ^{n + 1} )}{( 3 ^{n - 1} \cdot 9 ^{n - 1} )}

2 (x + 4) + 3 (2 x - 1) - 2 x

3 (5 + 8) (5 - w)

4 t^{2} - 36 b^{2}

- 1 + (- 6) + 8 x - 4

What is factor a^4+a^2b^2+25b^4 ?
The solution to factor a^4+a^2b^2+25b^4 is (a^2+5b^2+3ab)(a^2+5b^2-3ab)