Match Expressions: (-7-x)(a-13) and Its Equivalent Forms

To solve this problem, we'll follow these steps:

• Step 1: Expand each given expression using the distributive property.
• Step 2: Simplify the expressions obtained from expansion.
• Step 3: Compare the simplified expressions to the given expanded forms (a, b, and c).
• Step 4: Determine which expanded forms correspond to which original expressions and select the correct answer choice.

Let's begin with Step 1:
Expression 1: $(-7-x)(a-13)$

Expand:
$(-7)(a) + (-7)(-13) + (-x)(a) + (-x)(-13)$ = $-7a + 91 - ax + 13x$

Expression 2: $(-a+13)(-7-x)$

Expand:
$(-a)(-7) + (-a)(-x) + 13(-7) + 13(-x)$ = $7a + ax - 91 - 13x$

Expression 3: $(7+x)(a-13)$

Expand:
$7a - 91 + ax - 13x$

Now proceed with Step 3: Comparing these expanded expressions to the provided forms:

• Expression 1: $-7a + 91 - ax + 13x$ corresponds with Form b: $-7a + 91 - ax + 13x$.
• Expression 2: $7a + ax - 91 - 13x$ matches with Form a: $7a + ax - 91 - 13x$.
• Expression 3: $7a - 91 + ax - 13x$ is equivalent to Form a: $7a + ax - 91 - 13x$ after rearranging terms.

After comparing, we obtain the answer selection as 1-b, 2,3-a.