Answer
$-10x^{2}-5x^{2}y$
Work Step by Step
We are asked to subtract $(13x^{2}+x^{2}y-\frac{1}{4})$ from $(3x^{2}-4x^{2}y-\frac{1}{4})$. This is equivalent to $(3x^{2}-4x^{2}y-\frac{1}{4})-(13x^{2}+x^{2}y-\frac{1}{4})$.
To subtract two polynomials, we can add the opposite of the second polynomial to the first polynomial.
$(3x^{2}-4x^{2}y-\frac{1}{4})+(-13x^{2}-x^{2}y+\frac{1}{4})$
Next, we can combine like terms.
$(3x^{2}-13x^{2})+(-4x^{2}y-x^{2}y)+(-\frac{1}{4}+\frac{1}{4})=-10x^{2}-5x^{2}y$
