To simplify the given expression, let's carefully combine like terms step by step. The expression we need to simplify is:
[tex]\[ (2 x^2 - 4 x + 3 y - 6) + (4 y^2 - 3 x - 7 y + 4) \][/tex]
First, let's expand the parentheses (if needed) and write down the terms sequentially:
[tex]\[ 2 x^2 - 4 x + 3 y - 6 + 4 y^2 - 3 x - 7 y + 4 \][/tex]
Next, let's group the terms with the same variables together:
For [tex]\(x^2\)[/tex] terms:
[tex]\[ 2 x^2 \][/tex]
For [tex]\(x\)[/tex] terms:
[tex]\[ -4 x - 3 x = -7 x \][/tex]
For [tex]\(y^2\)[/tex] terms:
[tex]\[ 4 y^2 \][/tex]
For [tex]\(y\)[/tex] terms:
[tex]\[ 3 y - 7 y = -4 y \][/tex]
For the constant terms:
[tex]\[ -6 + 4 = -2 \][/tex]
Now, let's combine all these grouped terms to form the simplified expression:
[tex]\[ 2 x^2 - 7 x + 4 y^2 - 4 y - 2 \][/tex]
So, the simplified form of the given expression is:
[tex]\[ 2 x^2 - 7 x + 4 y^2 - 4 y - 2 \][/tex]
Thus, the correct simplified expression from the options provided is:
[tex]\[ 2 x^2 - 7 x + 4 y^2 - 4 y - 2 \][/tex]
