Which of the following are properties of a perfect square trinomial? Select all that apply.A.The second 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.SUBMITarrow_backPREVIOUS
Question
Which of the following are properties of a perfect square trinomial? Select all that apply.A.The second 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.SUBMITarrow_backPREVIOUS
Solution
The properties of a perfect square trinomial are:
A. The second and third terms do not necessarily have to be perfect squares. In a perfect square trinomial, the first and last terms are perfect squares.
B. It is not true that neither of the perfect squares can have a minus sign. A perfect square trinomial can be in the form (a+b)^2 or (a-b)^2. In the case of (a-b)^2, the trinomial would be a^2 - 2ab + b^2. So, a perfect square trinomial can have a minus sign.
C. This is correct. If the perfect square terms are A^2 and B^2 then the other term must be 2AB or –2AB. This is because a perfect square trinomial is the square of a binomial. So, it is in the form (A+B)^2 = A^2 + 2AB + B^2 or (A-B)^2 = A^2 - 2AB + B^2.
D. This is not correct because option C is a property of a perfect square trinomial.
So, the correct answer is C. If the perfect square terms are A^2 and B^2 then the other term must be 2AB or –2AB.
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