Answer:
1- The sum is: 2m + 2n + 7 = 2(m+n) + 7
2- The difference is: 3m - 2
3- The difference is: -2m - 2n + 2 = -2(m+n-1)
Step-by-step explanation:
Before we begin, remember the following:
+ve * +ve = +ve
-ve * -ve = -ve
+ve * -ve = -ve
-ve * +ve = -ve
Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree
Now, let's check the problems:
Problem 1:
Adding two polynomials:
(m + n + 3) + (m + n + 4)
We first start by getting rid of the brackets:
m + n + 3 + m + n + 4
Now, we add like terms:
2m + 2n + 7
As an additional step, we can take 2 as a common factor from the first two terms:
2(m+n) + 7
Problem 2:
Subtracting two polynomials:
(10m - 6) - (7m - 4)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
10m - 6 - 7m + 4
Now, we add/subtract like terms:
3m - 2
Problem 3:
Subtracting two polynomials:
(4m - 5) - (6m - 7 + 2n)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
4m - 5 - 6m + 7 - 2n
Now, we add/subtract like terms:
-2m - 2n + 2
As an additional step, we can take -2 as a common factor from the above expression:
-2(m+n-1)
Hope this helps :)