Question
What is the value of the expression \( (2 x+y)(2 x-y) \) when \( x=4 \) and \( y=-5 \) ?
Ask by Ward Lowe. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The value of the expression is 39.
Solution
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:** \( 39 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the value of the expression \( (2x + y)(2x - y) \) when \( x = 4 \) and \( y = -5 \), we first substitute the values of \( x \) and \( y \) into the expression. First, calculate \( 2x \): \[ 2x = 2 \cdot 4 = 8 \] Now substitute \( 2x \) and \( y \) into the expression: \[ (2x + y) = 8 + (-5) = 8 - 5 = 3 \] \[ (2x - y) = 8 - (-5) = 8 + 5 = 13 \] Now multiply these two results together: \[ (2x + y)(2x - y) = 3 \cdot 13 = 39 \] Thus, the value of the expression \( (2x + y)(2x - y) \) when \( x = 4 \) and \( y = -5 \) is \( \boxed{39} \).
