Question

which expression can be used to find the difference of the polynomials?

\\((4m - 5) - (6m - 7 + 2n)\\)

\\(\bigcirc\\ (4m - 5) + (6m + 7 + 2n)\\)
\\(\bigcirc\\ (4m - 5) + (-6m + 7 + 2n)\\)
\\(\bigcirc\\ (4m - 5) + (-6m - 7 - 2n)\\)
\\(\bigcirc\\ (4m - 5) + (-6m + 7 - 2n)\\)

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Distribute the negative sign

To subtract a polynomial, we add its opposite. This means we distribute the negative sign (or multiply by \(-1\)) to every term inside the second set of parentheses:

$$ -(6m - 7 + 2n) = -6m + 7 - 2n $$

Step 2: Rewrite as addition

Now, replace the subtraction of the polynomial with the addition of its opposite terms:

$$ (4m - 5) + (-6m + 7 - 2n) $$

Answer:

$$ (4m - 5) + (-6m + 7 - 2n) $$

(This corresponds to the fourth option)