What is the value of the expression $$ (2 x+y)(2 x-y) $$ when $$ x=4 $$ and $$ y=-5 $$ ?

Question

UpStudy AI · Accepted Answer

To evaluate the expression $$ (2x + y)(2x - y) $$ with $$ x = 4 $$ and $$ y = -5 $$, follow these steps:

1. **Substitute the values of $$ x $$ and $$ y $$ into the expression:**

$$
   (2(4) + (-5))(2(4) - (-5))
   $$

2. **Simplify each part inside the parentheses:**

- First parenthesis:
     $$
     2(4) + (-5) = 8 - 5 = 3
     $$
   
   - Second parenthesis:
     $$
     2(4) - (-5) = 8 + 5 = 13
     $$

3. **Multiply the results from the two parentheses:**

$$
   3 \times 13 = 39
   $$

**Final Answer:** $$ 39 $$
The value of the expression is 39.

What is the value of the expression \( (2 x+y)(2 x-y) \) when \( x=4 \) and \( y=-5 \) ?