5
AssignmentMultiple Select

Introduction to Polynomials

Question 5 • Common Core Algebra I B-IC

Which products result in a difference of squares? Check all that apply.(5z + 3)(–5z – 3)(w – 2.5)(w + 2.5)(8g + 1)(8g + 1)(–4v – 9)(–4v + 9)(6y + 7)(7y – 6)(p – 5)(p – 5)

Answer
A
(5z + 3)(–5z – 3)
B
(w – 2.5)(w + 2.5)
C
(8g + 1)(8g + 1)
D
(–4v – 9)(–4v + 9)
E
(6y + 7)(7y – 6)
F
(p – 5)(p – 5)

Explanation

A difference of squares comes from multiplying conjugates: (a − b)(a + b) = a² − b². Choice B gives (w − 2.5)(w + 2.5) = w² − 6.25, and choice D gives (−4v − 9)(−4v + 9) = 16v² − 81. The other products are not conjugate pairs; for example, choice A multiplies a binomial by its negative, producing a negative square.

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