Question

1. What is the sum of the polynomials?

(m + n + 3) + (m + n + 4)

2. Find the difference of the polynomials
(10m – 6) – (7m – 4)

3. Find the difference of the polynomials
(4m – 5) – (6m – 7 + 2n)

Answer 1

The sum of the polynomials (m + n + 3) and (m + n + 4) is 2m + 2n + 7. The difference of the polynomials (10m – 6) and (7m – 4) is 3m - 2. The difference of the polynomials (4m – 5) and (6m – 7 + 2n) is -2m - 2n - 2.

Step-by-step explanation:

To find the sum of the polynomials (m + n + 3) and (m + n + 4), we simply combine like terms:

(m + n + 3) + (m + n + 4)
= m + m + n + n + 3 + 4
= 2m + 2n + 7.

To find the difference of the polynomials (10m – 6) and (7m – 4), we subtract the second polynomial from the first:

(10m – 6) – (7m – 4)
= 10m - 7m - 6 + 4
= 3m - 2.

Lastly, to find the difference of the polynomials (4m – 5) and (6m – 7 + 2n), we again subtract the second polynomial from the first:

(4m – 5) – (6m – 7 + 2n)
= 4m - 6m + 5 - 7 - 2n
= -2m - 2n - 2.

Answer 2

1. 2m+2n+7

2. 3m-2

3.-2m+2-2n

Explanation:

To find the sum of given polynomials (m+n+3) +(m+n+4)

Firstly, open the parenthesis we will get m+n+3+m+n+4

After simplification we will get 2m+2n+7

To find the difference of given polynomials (10m-6)-(7m-4)

Firstly, open the parenthesis we will get 10m-6-7m+4

After simplification we will get 3m-2

Again to find the difference of the polynomials (4m-5)-(6m-7+2n)

Firstly, open the parenthesis we will get 4m-5-6m+7-2n

After simplification we will get -2m+2-2n