Question

multiply (x - 4)(2x + 3) using the foil method. select the answer choice showing the foil method products.

a. (x)(2x + 3) + (x - 4)

b. (x - 4)(2x) + (2x)(3)

c. (x)(2x) + 3(x) + (-4)(2x) + (-4)(3)

d. (x - 4)(2x) + (x - 4)(3)

Explanation:

Step1: Recall FOIL Method

FOIL stands for First, Outer, Inner, Last. For \((a + b)(c + d)\), it's \(a\cdot c + a\cdot d + b\cdot c + b\cdot d\). Here, \(a = x\), \(b=-4\), \(c = 2x\), \(d = 3\).

Step2: Apply FOIL to \((x - 4)(2x + 3)\)

• First: \(x\cdot2x\)
• Outer: \(x\cdot3\)
• Inner: \(-4\cdot2x\)
• Last: \(-4\cdot3\)

So the products are \((x)(2x)+3(x)+(-4)(2x)+(-4)(3)\), which matches option C.

Answer:

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