Questions: Rewrite the expression so that the terms have a common binomial factor. a(x-2)+b(2-x)

Rewrite the expression so that the terms have a common binomial factor. a(x-2)+b(2-x)
Transcript text: Rewrite the expression so that the terms have a common binomial factor. \[ a(x-2)+b(2-x) \]
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Solution

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Solution Steps

Step 1: Identify the Expression

The given expression is: \[ a(x-2) + b(2-x) \]

Step 2: Rewrite the Expression

Notice that \(2-x\) can be rewritten as \(-(x-2)\). Therefore, the expression becomes: \[ a(x-2) - b(x-2) \]

Step 3: Factor Out the Common Binomial

Now that both terms have a common binomial factor \((x-2)\), we can factor it out: \[ (a-b)(x-2) \]

Final Answer

The expression with a common binomial factor is: \[ \boxed{(a-b)(x-2)} \]

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