Question

what is the difference of the two polynomials?\\((7y^2 + 6xy) - (-2xy + 3)\\)\\(\bigcirc\\ 7y^2 + 4xy - 3\\)\\(\bigcirc\\ 7y^2 + 8xy - 3\\)\\(\bigcirc\\ 7y^2 + 4xy + 3\\)\\(\bigcirc\\ 7y^2 + 8xy + 3\\)

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial, we distribute the negative sign to each term inside the parentheses:
$(7y^2 + 6xy) - (-2xy + 3) = 7y^2 + 6xy + 2xy - 3$

Step2: Combine like terms

Combine the $xy$-terms:
$6xy + 2xy = 8xy$

The $y^2$-term ($7y^2$) and the constant term ($-3$) remain unchanged. So the simplified form is:
$7y^2 + 8xy - 3$

Answer:

B. \( 7y^2 + 8xy - 3 \)