Which of the following are properties of a perfect square trinomial? Select all that apply.A.The first and third terms must be perfect squares.B.Neither of the perfect squares can have a minus sign.C.If the perfect square terms are A2 and B2 then the other term must be 2AB or –2AB.D.None of the above is a property of a perfect square trinomial.
Question
Which of the following are properties of a perfect square trinomial? Select all that apply.A.The first and third terms must be perfect squares.B.Neither of the perfect squares can have a minus sign.C.If the perfect square terms are A2 and B2 then the other term must be 2AB or –2AB.D.None of the above is a property of a perfect square trinomial.
Solution
The properties of a perfect square trinomial are:
A. The first and third terms must be perfect squares. This is because a perfect square trinomial is the square of a binomial. So, the first and third terms are the squares of the terms in the binomial.
B. Neither of the perfect squares can have a minus sign. This is true because a square of a number is always positive.
C. If the perfect square terms are A2 and B2 then the other term must be 2AB or –2AB. This is also true because a perfect square trinomial is of the form (A+B)² = A² + 2AB + B² or (A-B)² = A² - 2AB + B².
So, all of the options A, B, and C are properties of a perfect square trinomial.
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