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:

Step1: Distribute the negative sign

To rewrite the subtraction of polynomials 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 applying the negative sign:
$(4m - 5) + (-6m + 7 - 2n)$

Answer:

$\boldsymbol{(4m - 5) + (-6m + 7 - 2n)}$ (the fourth option)