Which is the complete factorization of 9x² - 25?

The expression $9x^2-25$ is a difference of squares: $(3x)^2-5^2=(3x-5)(3x+5)$, choice A. Check by multiplying: $(3x-5)(3x+5)=9x^2+15x-15x-25=9x^2-25$. Choice C, $(3x-5)^2$, expands to $9x^2-30x+25$, which has a middle term and a positive constant. Choice B expands to $9x^2-16x-25$. Choice D expands to $9x^2+40x-25$. Only choice A produces the original expression with no middle term, because the cross terms cancel in a difference of squares. The factored form is correct only if multiplying it out gives back the original expression exactly.