The subtraction of two polynomials, A;and B, is shown.

 A − B = C

If A = 6m + 2n − 1 and C = 14m + 26n − 31, which expression represents polynomial B?

A
20m + 28n − 32
B
−8m − 24n + 30
C
−32m + 30
D
8m + 24n − 30


We are given that:

\[
A - B = C
\]

Where:

\[
A = 6m + 2n - 1
\]
\[
C = 14m + 26n - 31
\]

We need to solve for \( B \). Rearranging the given equation, we get:

\[
B = A - C
\]

Now, let's subtract \( C \) from \( A \):

\[
B = (6m + 2n - 1) - (14m + 26n - 31)
\]

Distribute the negative sign:

\[
B = 6m + 2n - 1 - 14m - 26n + 31
\]

Now, combine like terms:

\[
B = (6m - 14m) + (2n - 26n) + (-1 + 31)
\]

This simplifies to:

\[
B = -8m - 24n + 30
\]

Thus, the correct expression for polynomial \( B \) is:

\[
\boxed{B = -8m - 24n + 30}
\]

So, the correct answer is **Option B**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you subtract two polynomials step by step?
2. How do you distribute a negative sign across a polynomial?
3. What are the key differences between addition and subtraction of polynomials?
4. How do you combine like terms in a polynomial?
5. Can you describe the process of simplifying a polynomial expression?

**Tip:** Always combine like terms (those with the same variables raised to the same powers) when simplifying polynomials.

The subtraction of two polynomials, A and B, is shown.

A − B = C

If A = 6m + 2n − 1 and C = 14m + 26n − 31, which expression represents polynomial B?

A) 20m + 28n − 32
B) −8m − 24n + 30
C) −32m + 30
D) 8m + 24n − 30

Learn how to subtract two polynomials in this problem where A = 6m + 2n - 1 and C = 14m + 26n - 31. Solve for polynomial B using the distributive property and combining like terms. Suitable for students in Grades 7-10.

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