Factoring the polynomial

Question

Factor the polynomial if it is a perfect square trinomial, or state that the polynomial is prime.

36x² - 60xy + 25y²

Answer 1

(ax+by)² = a²x² + 2abx + b²y² From the x² and y² terms it is clear that a = sqrt(36) = ± 6 and b = sqrt(25) = ±5.

to show that this is a perfect square, you have to show that -60 = 2ab This works for a = -6 b = 5 and a= 6 and b = -5. There are two solutions:

(6x - 5y)² and (-6x + 5y)²

Answer 2

(6x-5y)^2

=(6x-5y)(6x-5y)

= the perfect square trinomial in factored form

or (5y-6x)^2