What is factor a^2b^4-81 ?

The solution to factor a^2b^4-81 is (ab^2+9)(ab^2-9)

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factor a^2b^4-81

factor

a^{2} b^{4} - 81

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

Solution steps

a^{2} b^{4} - 81

a^{2} b^{4} = (a b^{2})^{2}

81 = 9^{2}

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

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

(- 6)^{1}

∣ 0 ∣ - 4

11 - (- 9)

(4 9^{\frac{1}{2}})^{4}

\frac{3}{40}