Question

kate multiplied two binomials using the distributive property. she made a mistake in one of the steps. where did she first make a mistake?

$(x - 2)(3x + 4)$

1. $(x - 2)(3x) + (x - 2)(4)$

1. $(x)(3x) + (2)(3x) + (x)(4) + (2)(4)$

1. $3x^2 + 6x + 4x + 8$

1. $3x^2 + 10x + 8$

\bigcirc a. step 4

\bigcirc b. step 1

\bigcirc c. step 2

\bigcirc d. step 3

Explanation:

Step1: Analyze Step 1

Using the distributive property (FOIL or distribution), \((x - 2)(3x + 4)\) can be written as \((x - 2)(3x)+(x - 2)(4)\), so Step 1 is correct.

Step2: Analyze Step 2

When distributing \((x - 2)(3x)\), it should be \(x(3x)+(-2)(3x)\), and for \((x - 2)(4)\), it should be \(x(4)+(-2)(4)\). But in Step 2, it's written as \((x)(3x)+(2)(3x)+(x)(4)+(2)(4)\) (the sign of -2 is missed, it should be -2 instead of +2 in the distribution). So Step 2 has the first mistake.

Step3: Confirm with later steps (optional)

Even though later steps have errors, the first mistake is in Step 2.

Answer:

C. Step 2