Multiplying Monomials and Binomials — Quiz

Question 5 • Algebra I

Which products result in a perfect square trinomial? Choose three correct answers.

Answer

open paren 2 x minus 3 close paren times open paren negative 3 plus 2 x close paren

open paren 16 minus x squared close paren times open paren x squared minus 16 close paren

open paren 4 y squared plus 25 close paren times open paren 25 plus 4 y squared close paren

open paren x y plus x close paren times open paren x y plus x close paren

open paren negative x plus 9 close paren times open paren negative x minus 9 close paren

Explanation

A has identical factors, so (2x − 3)² expands to 4x² − 12x + 9, a perfect square trinomial. C also has identical factors: (4y² + 25)² expands to 16y⁴ + 200y² + 625. D is (xy + x)², which expands to x²y² + 2x²y + x². In B the factors are opposites, so their product is negative, and E is a difference of squares that gives a binomial, not a trinomial.

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