Determine whether the polynomial is a difference of squares, and if it is, factor it.

\[ y^2 - 25 \]

A. Is not a difference of squares

B. Is a difference of squares: \((y - 5)^2\)

C. Is a difference of squares: \((y + 5)(y - 5)\)

D. Is a difference of squares: \((y + 5)^2\)

the answer is C y² - 25 = y² - 5² = (y + 5)(y - 5) which is a difference of two squares

Answered by Poknoy | 2024-06-10

Answer:
Option: C is the correct answer.
C. Is a difference of squares: (y + 5)(y − 5).
Step-by-step explanation:
We are given a polynomial expression in terms of the variable y as follows:
y 2 − 25
Now this expression could also be written as:
y 2 − 25 = y 2 − 5 2
This means that the expression is a difference of squares.
Also, we know that:
a 2 − b 2 = ( a + b ) ( a − b )
Here,
a = y an d b = 5
Hence,
y 2 − 25 = ( y + 5 ) ( y − 5 )

Answered by lidaralbany | 2024-06-12

The polynomial y 2 − 25 is a difference of squares because it can be written as y 2 − 5 2 . It can be factored into ( y + 5 ) ( y − 5 ) . Therefore, the correct choice is option C.
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Answered by lidaralbany | 2025-01-31