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.

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

What is the standard form of a perfect square trinomial?

Back

The standard form of a perfect square trinomial is a² + 2ab + b², which factors to (a + b)².

Front

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

Back

No, because the middle term (18) is not equal to 2 times the product of the square roots of the first (1) and last (9) terms.

Front

What is the factored form of x² + 24x + 144?

Back

(x + 12)².

Front

What is the result of expanding (x + 6)²?

Back

x² + 12x + 36.

Front

Is x² + 10x + 100 a perfect square trinomial?

Back

No, because the middle term (10) is not equal to 2 times the product of the square roots of the first (1) and last (100) terms.

Front

What are the steps to factor a perfect square trinomial?

Back

1. Identify the first and last terms as perfect squares. 2. Check if the middle term is twice the product of the square roots of the first and last terms. 3. Write the factored form as (a + b)².

Front

What is the square of (x + 4)?

Back

(x + 4)² = x² + 8x + 16.

Front

What is the relationship between the coefficients in a perfect square trinomial?

Back

In a perfect square trinomial a² + 2ab + b², the coefficient of the middle term (2ab) is equal to twice the product of the coefficients of the first and last terms.