Question

which line shows the correct and complete distribution for the problem below?
$(2x + 3)(3x - 1)$
(1 point)
○ $2x \cdot 3x + 3 \cdot 3x$
○ $2x \cdot 3 + 3x \cdot -1$
○ $2x \cdot 3x + 2x \cdot -1 + 3 \cdot 3x + 3 \cdot -1$
○ $2x \cdot 3x - 2x \cdot -1 - 3 \cdot 3x - 3 \cdot -1$

Explanation:

Step1: Recall the distributive property (FOIL method)

For \((a + b)(c + d)\), the distribution is \(a\cdot c + a\cdot d + b\cdot c + b\cdot d\). Here, \(a = 2x\), \(b = 3\), \(c = 3x\), \(d=-1\).

Step2: Apply the distributive property

Substitute the values into the formula: \(2x\cdot3x + 2x\cdot(-1)+3\cdot3x + 3\cdot(-1)\).

Answer:

\(2x\cdot3x + 2x\cdot -1 + 3\cdot3x + 3\cdot -1\) (the third option)