Question

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

Explanation:

Step1: Recall distributive property

The distributive property for multiplying two binomials \((a + b)(c + d)\) is \(a(c + d)+b(c + d)=ac+ad+bc+bd\). Here, \(a = x\), \(b=- 4\), \(c = 2x\), \(d = 3\).

Step2: Apply distributive property

Applying the distributive property to \((x - 4)(2x+3)\), we get \((x - 4)(2x)+(x - 4)(3)\) because we distribute \((x - 4)\) over \(2x\) and \(3\) in the binomial \((2x + 3)\).

Answer:

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