Question

1. let \\( p = 7y^2 - 2xy + 5x^2 \\) and \\( q = 3x^2 - 4y^2 \\).

match each expression with the correct polynomial.

	\\( 2x^2 - 2xy + 11y^2 \\)	\\( -2x^2 + 2xy - 11y^2 \\)	\\( 8x^2 - 2xy + 3y^2 \\)	\\( 10x^2 - 2xy + y^2 \\)
\\( p + q \\)	\\( \square \\)	\\( \square \\)	\\( \square \\)	\\( \square \\)

Explanation:

Step1: Calculate \( P - Q \)

Substitute \( P = 7y^2 - 2xy + 5x^2 \) and \( Q = 3x^2 - 4y^2 \) into \( P - Q \):

$$
LATEXBLOCK0
$$

Step2: Calculate \( P + Q \)

Substitute \( P = 7y^2 - 2xy + 5x^2 \) and \( Q = 3x^2 - 4y^2 \) into \( P + Q \):

$$
LATEXBLOCK1
$$

Answer:

For \( P - Q \), the correct polynomial is \( 2x^2 - 2xy + 11y^2 \) (check the box under \( 2x^2 - 2xy + 11y^2 \) for \( P - Q \)).

For \( P + Q \), the correct polynomial is \( 8x^2 - 2xy + 3y^2 \) (check the box under \( 8x^2 - 2xy + 3y^2 \) for \( P + Q \)).