Factoring Difference of Squares and Perfect Square Trinomials

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.

Front

How do you factor the expression 9n^2 + 1?

Back

9n^2 + 1 cannot be factored using the difference of squares.

Front

Factor the expression r^2 - 9t^2.

Back

r^2 - 9t^2 can be factored as (r + 3t)(r - 3t).

Front

What is the first step in factoring a difference of squares?

Back

The first step is to identify if the expression is in the form a^2 - b^2.

Front

How do you factor the expression 45x^2 - 20?

Back

45x^2 - 20 can be factored as 5(3x + 2)(3x - 2).

Front

What is the factored form of 4a^2 - 25?

Back

4a^2 - 25 can be factored as (2a + 5)(2a - 5).

Front

How do you recognize a perfect square trinomial?

Back

A perfect square trinomial can be recognized by its structure: it has three terms, and the first and last terms are perfect squares.

Front

What is the factored form of 25x^2 + 60x + 36?

Back

25x^2 + 60x + 36 can be factored as (5x + 6)^2.

Front

What is the significance of the coefficients in a perfect square trinomial?

Back

In a perfect square trinomial, the middle term is twice the product of the square roots of the first and last terms.