What is factor 81y^4-1 ?

The solution to factor 81y^4-1 is (9y^2+1)(3y+1)(3y-1)

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factor 81y^4-1

factor

81 y^{4} - 1

(9 y^{2} + 1) (3 y + 1) (3 y - 1)

Solution steps

81 y^{4} - 1

Apply exponent rules

= (9 y^{2})^{2} - 1^{2}

Apply Difference of Two Squares Formula:

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

(9 y^{2})^{2} - 1^{2} = (9 y^{2} + 1) (9 y^{2} - 1)

= (9 y^{2} + 1) (9 y^{2} - 1)

Factor

9 y^{2} - 1 : (3 y + 1) (3 y - 1)

= (9 y^{2} + 1) (3 y + 1) (3 y - 1)

\frac{40 x ^{8} y ^{2}}{24 x ^{7} y ^{5}}

9 y^{2} - 24 y + 16

5 (x + 2) + 4 x = 6 x + 1

\frac{- 12}{- 2}

6 x^{3} + 18 x^{2} - 8 x - 24