Flashcard 0.5 - Factoring Perfect Square Trinomials & Grouping

A perfect square trinomial is a quadratic expression that can be written in the form (a + b)² or (a - b)², which expands to a² ± 2ab + b².

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

(n + 5)².

(x - 12)².

(x + 9)².

The formula is a² ± 2ab + b² = (a ± b)².

1. Identify a² and b². 2. Check if the middle term is ±2ab. 3. Write the expression as (a ± b)².

The middle term must equal ±2 times the product of the square roots of the first and last terms for the trinomial to be a perfect square.

Yes, trinomials can often be factored using other methods, such as grouping or the quadratic formula.

A perfect square trinomial can be expressed as the square of a binomial, while a regular trinomial may not have this property.