Question

which expression can be used to find the difference of the polynomials?
(4m - 5) - (6m - 7 + 2n)
(4m - 5) + (6m + 7 + 2n)
(4m - 5) + (-6m + 7 + 2n)
(4m - 5) + (-6m - 7 - 2n)
(4m - 5) + (-6m + 7 - 2n)

Explanation:

Step1: Distribute the negative sign

To rewrite the subtraction as addition, distribute the negative sign to each term inside the second parentheses:
$(4m - 5) - (6m - 7 + 2n) = (4m - 5) + (-1)\times(6m) + (-1)\times(-7) + (-1)\times(2n)$

Step2: Simplify the distributed terms

Calculate each term after distributing the negative sign:
$(4m - 5) + (-6m + 7 - 2n)$

Answer:

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