Multiply and add like terms: $$ (-2 y-5)^{2} $$

Question

UpStudy AI · Accepted Answer

To expand and simplify the expression $$(-2y - 5)^2$$, you can use the formula for the square of a binomial:

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

Here, $$a = -2y$$ and $$b = -5$$. Applying the formula:

$$
(-2y - 5)^2 = (-2y)^2 + 2 \cdot (-2y) \cdot (-5) + (-5)^2
$$

Now, calculate each term:

1. **Square the first term:**
   $$
   (-2y)^2 = 4y^2
   $$

2. **Multiply the two terms and double the product:**
   $$
   2 \cdot (-2y) \cdot (-5) = 20y
   $$

3. **Square the second term:**
   $$
   (-5)^2 = 25
   $$

Combine all the terms:

$$
4y^2 + 20y + 25
$$

**Final Answer:**

$$
(-2y - 5)^2 = 4y^2 + 20y + 25
$$
$$ (-2y - 5)^2 = 4y^2 + 20y + 25 $$

Multiply and add like terms: \( (-2 y-5)^{2} \)