Question

Write each polynomial as a difference of squares
81-64=
Numbers
I 2
• Answer
=====♥
x*-9=
I 2
i Answer i
Variables
2
2
Expressions
Answer
4x2-25 =
Answer
Answer
2
2
Answer
:: 8
:: 5
÷9
:: 3
: 2x
:x

Answer 1

To express each polynomial as a difference of squares, we can use the identity \( a^2 - b^2 = (a - b)(a + b) \).

1. **81 - 64**
- This can be written as \( 9^2 - 8^2 \).
- So the expression \( 81 - 64 = 9^2 - 8^2 = (9 - 8)(9 + 8) = 1 \cdot 17 = 17 \).

2. **x² - 9**
- This can be written as \( x^2 - 3^2 \).
- So, \( x² - 9 = (x - 3)(x + 3) \).

3. **4x² - 25**
- This can be written as \( (2x)² - 5² \).
- So, \( 4x² - 25 = (2x - 5)(2x + 5) \).

So to summarize:
1. \( 81 - 64 = 17 \) when evaluated, or expressed as a difference of squares:
- \( 81 - 64 = (9 - 8)(9 + 8) \).
2. The expression \( x^2 - 9 = (x - 3)(x + 3) \).
3. The expression \( 4x^2 - 25 = (2x - 5)(2x + 5) \).