(2 + x)(y – z) = 

(a – b)(m – n) = 

(s + t)(x + y – 3) = 

(m + n + 1)(p – r – s) =

Let's expand each of the given expressions using the distributive property (also known as FOIL for binomials):

1. **(2 + x)(y – z):**

\[
(2 + x)(y – z) = 2(y – z) + x(y – z) = 2y – 2z + xy – xz = 2y – 2z + xy – xz
\]

2. **(a – b)(m – n):**

\[
(a – b)(m – n) = a(m – n) – b(m – n) = am – an – bm + bn = am – an – bm + bn
\]

3. **(s + t)(x + y – 3):**

\[
(s + t)(x + y – 3) = s(x + y – 3) + t(x + y – 3) = sx + sy – 3s + tx + ty – 3t = sx + sy – 3s + tx + ty – 3t
\]

4. **(m + n + 1)(p – r – s):**

\[
(m + n + 1)(p – r – s) = m(p – r – s) + n(p – r – s) + 1(p – r – s) 
= mp – mr – ms + np – nr – ns + p – r – s 
= mp – mr – ms + np – nr – ns + p – r – s
\]

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### Expanded results:
1. \((2 + x)(y – z) = 2y – 2z + xy – xz\)
2. \((a – b)(m – n) = am – an – bm + bn\)
3. \((s + t)(x + y – 3) = sx + sy – 3s + tx + ty – 3t\)
4. \((m + n + 1)(p – r – s) = mp – mr – ms + np – nr – ns + p – r – s\)

Would you like more details or have any questions?

### Related Questions:
1. How does the distributive property work for polynomials with more than two terms?
2. What happens when you expand expressions involving powers of variables?
3. Can you apply the distributive property to expressions with fractions?
4. How does the distributive property work with matrices or vectors in algebra?
5. Can you explain how factoring is the reverse of distribution?

### Tip:
When expanding expressions, carefully keep track of positive and negative signs to avoid mistakes in simplification!

(2 + x)(y – z) = (a – b)(m – n) = (s + t)(x + y – 3) = (m + n + 1)(p – r – s) =

Learn how to expand algebraic expressions like (2 + x)(y – z) and others using the distributive property. This step-by-step solution explains the process of multiplying binomials and simplifying the terms, suitable for students in Grades 8-10.

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