If xt ≠ 0, then which of the following equations is equivalent to 81x8 – 16t8 = 9x4 + 4t4?

Question

A.9x⁴ + 4t⁴ = 0

B.(3x² + 2t²)⁴ = 0

C.(3x² – 2t²)(3x² +2t²) = 1

D.(3x² – 2t²)(3x² +2t²)(​9x⁴ + 4t⁴) = 1

Answer 1

81x^8 -16t^8 = 9x^4 + 4t^4

(9x^4 -4t^4)(9x^4+4t^4) = 9x^4 + 4t^4

divide both sides by 9x^4 + 4t^4 gives:

9x^4 - 4t^4 = 1

factors as the general formula a^2 -b^2 = (a+b)(a-b) with a = 9x^2 and b = 2t^2

(3x^2 +2t^2)(3x^2 -2t^2) = 1

C is correct