Question

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

y2 − 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

Answer 1

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

Answer 2

Option: C is the correct answer.

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

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\ and\ b=5`

Hence,

`y^2-25=(y+5)(y-5)`