To find the sum of the given polynomials, follow these steps:
1. Write down the given polynomials:
- First polynomial: [tex]\( 8x^2 - 9y^2 - 4x \)[/tex]
- Second polynomial: [tex]\( x^2 - 3y^2 - 7x \)[/tex]
2. Combine the like terms:
- For the [tex]\( x^2 \)[/tex] terms: [tex]\( 8x^2 \)[/tex] and [tex]\( x^2 \)[/tex]
- For the [tex]\( y^2 \)[/tex] terms: [tex]\( -9y^2 \)[/tex] and [tex]\( -3y^2 \)[/tex]
- For the [tex]\( x \)[/tex] terms: [tex]\( -4x \)[/tex] and [tex]\( -7x \)[/tex]
3. Add the coefficients of like terms:
- [tex]\( 8x^2 + x^2 = 9x^2 \)[/tex]
- [tex]\( -9y^2 + (-3y^2) = -12y^2 \)[/tex]
- [tex]\( -4x + (-7x) = -11x \)[/tex]
4. Combine these results:
- The sum of the polynomials [tex]\( (8x^2 - 9y^2 - 4x) + (x^2 - 3y^2 - 7x) \)[/tex] is [tex]\( 9x^2 - 12y^2 - 11x \)[/tex]
Therefore, the sum of the given polynomials is [tex]\( 9x^2 - 12y^2 - 11x \)[/tex].
So, the correct answer is:
[tex]\[ 9x^2 - 12y^2 - 11x \][/tex]
