To find the difference of the polynomials [tex]\((12x^2 - 11y^2 - 13x) - (5x^2 - 14y^2 - 9x)\)[/tex], we need to subtract the corresponding coefficients of each term.
1. Subtract the [tex]\(x^2\)[/tex] terms:
[tex]\[
12x^2 - 5x^2 = (12 - 5)x^2 = 7x^2
\][/tex]
2. Subtract the [tex]\(y^2\)[/tex] terms:
[tex]\[
-11y^2 - (-14y^2) = -11y^2 + 14y^2 = (14 - 11)y^2 = 3y^2
\][/tex]
3. Subtract the [tex]\(x\)[/tex] terms:
[tex]\[
-13x - (-9x) = -13x + 9x = (-13 + 9)x = -4x
\][/tex]
By combining these results, the resulting polynomial is:
[tex]\[
7x^2 + 3y^2 - 4x
\][/tex]
Thus, the correct answer is [tex]\(7x^2 + 3y^2 - 4x\)[/tex].
