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

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 \( P + Q \)).