Kate multiplied two binomials using the distributive property. She made a mistake in one of the steps. Where did she first make a mistake? $$ (x-2)(3 x+4) $$ 1. $$ (x-2)(3 x)+(x-2)(4) $$ 2. $$ (x)(3 x)+(2)(3 x)+(x)(4)+(2)(4) $$ 3. $$ 3 x^{2}+6 x+4 x+8 $$ 4. $$ 3 x^{2}+10 x+8 $$ A. Step 1 B. Step 3 C. Step 4 D. Step 2

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Let's analyze Kate's steps in multiplying the binomials $$(x - 2)(3x + 4)$$:

1. **Step 1:** $$ (x-2)(3x) + (x-2)(4) $$  
   - **Correct:** This step correctly applies the distributive property by multiplying each term in the first binomial by each term in the second binomial.

2. **Step 2:** $$ (x)(3x) + (2)(3x) + (x)(4) + (2)(4) $$  
   - **Incorrect:** Here, Kate should multiply $$(-2)$$ instead of $$2$$. The correct expansion should be:
     $$
     (x)(3x) + (-2)(3x) + (x)(4) + (-2)(4)
     $$
     This mistake leads to the wrong signs in the subsequent terms.

3. **Step 3:** $$ 3x^{2} + 6x + 4x + 8 $$  
   - This follows from step 2, but since step 2 was incorrect, this step is also affected.

4. **Step 4:** $$ 3x^{2} + 10x + 8 $$  
   - This is the final incorrect result based on the previous errors.

**Conclusion:** Kate first made a mistake in **Step 2** by incorrectly using $$2$$ instead of $$-2$$.

**Answer:** D. Step 2
Kate first made a mistake in Step 2 by incorrectly using 2 instead of -2.

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