Final Answer:
The perfect square trinomial for (a-b)² is a² - 2ab + b².
Step-by-step explanation:
A perfect square trinomial is a quadratic expression that can be factored into a square of a binomial. For the binomial (a-b)², the expanded form is obtained by squaring each term of the binomial. This results in (a-b)² = (a-b)(a-b) = a² - 2ab + b².
The expanded expression a² - 2ab + b² is considered a perfect square trinomial because it can be factored into the square of the binomial (a-b). To verify this, you can use the distributive property to multiply the factors (a-b)(a-b) and simplify to confirm that it equals a² - 2ab + b².
In summary, the perfect square trinomial for (a-b)² is a² - 2ab + b², where each term represents the squared form of the binomial (a-b). Understanding the expansion of perfect square trinomials is fundamental in algebra, providing a concise representation for certain quadratic expressions.