What is factor (ab)^4-81 ?

The solution to factor (ab)^4-81 is (a^2b^2+9)(ab+3)(ab-3)

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factor (ab)^4-81

factor

(ab)^{4} - 81

(a^{2} b^{2} + 9) (ab + 3) (ab - 3)

Solution steps

(ab)^{4} - 81

(ab)^{4} = ((ab)^{2})^{2}

81 = 9^{2}

= ((ab)^{2})^{2} - 9^{2}

Apply Difference of Two Squares Formula:

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

((ab)^{2})^{2} - 9^{2} = ((ab)^{2} + 9) ((ab)^{2} - 9)

= ((ab)^{2} + 9) ((ab)^{2} - 9)

Factor

(ab)^{2} - 9 : (ab + 3) (ab - 3)

= ((ab)^{2} + 9) (ab + 3) (ab - 3)

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

= (a^{2} b^{2} + 9) (ab + 3) (ab - 3)

(\frac{6 n ^{2}}{3 n})^{- 3}

(b - c)^{3} + (c - a)^{3} + (a - b)^{3}

x^{6} - 27 y^{3}

x - 4 = 10

69 (\frac{π}{180})

What is factor (ab)^4-81 ?
The solution to factor (ab)^4-81 is (a^2b^2+9)(ab+3)(ab-3)