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 the like terms in each polynomial.
1. Identify like terms in the polynomials:
- The terms involving [tex]\(x^2\)[/tex]: [tex]\(12x^2\)[/tex] and [tex]\(5x^2\)[/tex]
- The terms involving [tex]\(y^2\)[/tex]: [tex]\(-11y^2\)[/tex] and [tex]\(-14y^2\)[/tex]
- The terms involving [tex]\(x\)[/tex]: [tex]\(-13x\)[/tex] and [tex]\(-9x\)[/tex]
2. Subtract the coefficients of the like terms:
- For [tex]\(x^2\)[/tex]: [tex]\(12x^2 - 5x^2 = 7x^2\)[/tex]
- For [tex]\(y^2\)[/tex]: [tex]\(-11y^2 - (-14y^2) = -11y^2 + 14y^2 = 3y^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(-13x - (-9x) = -13x + 9x = -4x\)[/tex]
3. Combine the results:
- The difference of the polynomials is: [tex]\(7x^2 + 3y^2 - 4x\)[/tex]
So, the resulting polynomial after subtracting the given polynomials is:
[tex]\[
7x^2 + 3y^2 - 4x
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{7x^2 + 3y^2 - 4x}
\][/tex]
