Which expression represents a difference of squares?

Which expression represents a difference of squares?

• A. a^2 + b^2
• B. (a - b)^2
• C. (a + b)^2
• D. a^2 - b^2

Answer: (D)

A difference of squares occurs when you have one squared term minus another squared term, and it factors as (a − b)(a + b). The expression a^2 − b^2 fits that pattern, since it is exactly a^2 minus b^2 and can be factored as (a − b)(a + b). Expanding that product gives a^2 − b^2, with the cross terms canceling out. The other forms don’t represent a difference of squares. A^² + b^² is a sum of squares and does not factor into real linear factors. Squaring a binomial, as in (a − b)^2 or (a + b)^2, yields a^2 − 2ab + b^2 or a^2 + 2ab + b^2, which include the cross term ±2ab, not just a^2 − b^2.

A difference of squares occurs when you have one squared term minus another squared term, and it factors as (a − b)(a + b). The expression a^2 − b^2 fits that pattern, since it is exactly a^2 minus b^2 and can be factored as (a − b)(a + b). Expanding that product gives a^2 − b^2, with the cross terms canceling out.

The other forms don’t represent a difference of squares. A^² + b^² is a sum of squares and does not factor into real linear factors. Squaring a binomial, as in (a − b)^2 or (a + b)^2, yields a^2 − 2ab + b^2 or a^2 + 2ab + b^2, which include the cross term ±2ab, not just a^2 − b^2.