Question

question 9 of 10 multiply (x - 3)(4x + 2) using the distributive property. select the answer choice showing the correct distribution. a. (x)(4x + 2) + (x - 3) b. (x - 3)(4x) + (4x)(2) c. (x - 3)(4x) + (x - 3)(2) d. (x)(4x) + 2(x) + 4x + 2

Explanation:

Step1: Recall distributive property

The distributive property for multiplying a binomial by another binomial \((a + b)(c + d)=a(c + d)+b(c + d)\) (or equivalently \((a + b)(c + d)=ac+ad+bc+bd\)). Here, we have \((x - 3)(4x + 2)\), so we can treat \(x-3\) as the first binomial and \(4x + 2\) as the second binomial. Using the distributive property \(a(b + c)=ab+ac\) where \(a=(x - 3)\), \(b = 4x\) and \(c=2\), we get \((x - 3)(4x)+(x - 3)(2)\).

Step2: Analyze each option

• Option A: \((x)(4x + 2)+(x - 3)\) is incorrect because it does not distribute \(x-3\) over \(4x + 2\) properly.
• Option B: \((x - 3)(4x)+(4x)(2)\) is incorrect because the second term should be \((x - 3)(2)\) not \((4x)(2)\).
• Option C: \((x - 3)(4x)+(x - 3)(2)\) follows the distributive property as we derived.
• Option D: \((x)(4x)+2(x)+4x + 2\) is incorrect as it misapplies the distributive property.

Answer:

C. \((x - 3)(4x)+(x - 3)(2)\)