What is factor a^4-7a^2b^2+b^4 ?

The solution to factor a^4-7a^2b^2+b^4 is (a^2+b^2+3ab)(a^2+b^2-3ab)

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factor a^4-7a^2b^2+b^4

factor

a^{4} - 7 a^{2} b^{2} + b^{4}

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

Solution steps

a^{4} - 7 a^{2} b^{2} + b^{4}

Add and subtract

9 a^{2} b^{2}

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

Factor

a^{4} + 2 a^{2} b^{2} + b^{4} : (a^{2} + b^{2})^{2}

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

Apply exponent rules

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

Factor

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

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

(\frac{x ^{2}}{y ^{2}})^{2} - 1 - (\frac{y ^{2}}{x ^{2}})^{2}

x^{6} + 2 x^{2} + x^{2}

4 (6 f - 5) + 8 f

\frac{( 16 \cdot ( x + 1 ) ^{4} - x - 1 )}{( x + 2 )}

24 a^{3} + 37 a^{2} - 5 a

What is factor a^4-7a^2b^2+b^4 ?
The solution to factor a^4-7a^2b^2+b^4 is (a^2+b^2+3ab)(a^2+b^2-3ab)