Select the polynomial that is a perfect square trinomial.Group of answer choices9x2 + 9x + 136b2 − 24b + 816x2 + 24x + 94a2 − 10a + 25
Question
Select the polynomial that is a perfect square trinomial.
Group of answer choices
9x^2 + 9x + 13
6b^2 − 24b + 81
6x^2 + 24x + 9
4a^2 − 10a + 25
Solution
The perfect square trinomial from the given options is 4a^2 - 10a + 25.
Here's why:
A perfect square trinomial is a trinomial that can be written as (ax+b)^2 or (ax-b)^2.
In the case of 4a^2 - 10a + 25, it can be written as (2a - 5)^2.
Here's the step-by-step breakdown:
- The square root of 4a^2 is 2a.
- The square root of 25 is 5.
- The middle term is negative, so we use (ax - b)^2.
- The 22a5 gives us the middle term -10a.
So, 4a^2 - 10a + 25 is a perfect square trinomial.
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