1) Find the square. Simplify your answer. $$ \cdot(4 v-3)^{2} $$

Question

UpStudy AI · Accepted Answer

To find and simplify the square of the expression $$ (4v - 3)^2 $$, follow these steps:

### Step 1: Apply the Formula for Squaring a Binomial
The formula for squaring a binomial $$ (a - b)^2 $$ is:

$$
(a - b)^2 = a^2 - 2ab + b^2
$$

### Step 2: Identify $$ a $$ and $$ b $$
In the expression $$ (4v - 3)^2 $$:

- $$ a = 4v $$
- $$ b = 3 $$

### Step 3: Substitute $$ a $$ and $$ b $$ into the Formula

$$
(4v - 3)^2 = (4v)^2 - 2 \times (4v) \times 3 + 3^2
$$

### Step 4: Calculate Each Term

1. **First Term:** $$ (4v)^2 = 16v^2 $$
2. **Second Term:** $$ 2 \times (4v) \times 3 = 24v $$
3. **Third Term:** $$ 3^2 = 9 $$

### Step 5: Combine the Terms

$$
(4v - 3)^2 = 16v^2 - 24v + 9
$$

### Final Answer

$$
16v^2 - 24v + 9
$$
$$ 16v^2 - 24v + 9 $$

1) Find the square. Simplify your answer. \( \cdot(4 v-3)^{2} \)