Let's determine the difference of the given polynomials step-by-step.
We are given two polynomials:
[tex]\[
P_1 = 12x^2 - 11y^2 - 13x
\][/tex]
[tex]\[
P_2 = 5x^2 - 14y^2 - 9x
\][/tex]
We need to find the difference [tex]\( P_1 - P_2 \)[/tex].
1. Subtract the coefficients of [tex]\( x^2 \)[/tex]:
[tex]\[
12x^2 - 5x^2 = 7x^2
\][/tex]
2. Subtract the coefficients of [tex]\( y^2 \)[/tex]:
[tex]\[
-11y^2 - (-14y^2) = -11y^2 + 14y^2 = 3y^2
\][/tex]
3. Subtract the coefficients of [tex]\( x \)[/tex]:
[tex]\[
-13x - (-9x) = -13x + 9x = -4x
\][/tex]
Therefore, the difference of the polynomials is:
[tex]\[
7x^2 + 3y^2 - 4x
\][/tex]
So the correct answer is:
[tex]\[
7x^2 + 3y^2 - 4x
\][/tex]
Given the options, the correct one is:
[tex]\[
7x^2 + 3y^2 - 4x
\][/tex]
