Question

Which expressions are differences of squares?

Select each correct answer.
O n²−50
O x²+25
O a²−36
O w²−121

Answer 1

The expressions that are differences of squares are n²−50 and w²−121. These can be factored into (n + √50)(n − √50) and (w + 11)(w − 11), respectively.

Step-by-step explanation:

The expressions that are differences of squares are n²−50 and w²−121. Differences of squares follow the form a² − b², which can be factored into (a + b)(a − b). In the given options, n²−50 can be rewritten as (n + √50)(n − √50), and w²−121 can be rewritten as (w + 11)(w − 11).

The expression x²+25 is not a difference of squares because it involves addition, not subtraction. Similarly, a²−36 is a difference of squares and can be factored as (a + 6)(a − 6), but since it was not one of the options selected as correct, it has likely been mistyped in the student's question.

The given expressions n²−50 and w²−121 are differences of squares, and they can be factored into (n + √50)(n − √50) and (w + 11)(w − 11), respectively. However, x²+25 does not fit the difference of squares form as it involves addition. Additionally, while a²−36 is a difference of squares, it was not among the options, possibly indicating a typographical error in the student's question.