Factoring Perfect Square Trinomials

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It has the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

How can you identify a perfect square trinomial?

Back

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.

Front

Is x² + 18x + 9 a perfect square trinomial?

Back

No

Front

Is x² + 14x + 49 a perfect square trinomial?

Back

Yes

Front

Factor the trinomial x² - 30x + 225.

Back

(x - 15)²

Front

Factor the trinomial x² - 20x + 100.

Back

(x - 10)²

Front

Factor the trinomial x² - 4x + 4.

Back

(x - 2)²

Front

What is the general form of a perfect square trinomial?

Back

The general form is a² ± 2ab + b².

Front

What are the steps to factor a perfect square trinomial?

Back

1. Identify a², b², and 2ab. 2. Check if the middle term equals 2ab. 3. Write the factored form as (a ± b)².

Front

What is the square of (x + 3)?

Back

(x + 3)² = x² + 6x + 9.