factoring perfect square and difference of square trinomials

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, typically in the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

Factor the trinomial: 25x² + 60x + 36

Back

(5x + 6)²

Front

What is the formula for the difference of squares?

Back

The difference of squares can be factored using the formula a² - b² = (a + b)(a - b).

Front

Factor the expression: 25x² - 81

Back

(5x + 9)(5x - 9)

Front

What is the first step in factoring a perfect square trinomial?

Back

Identify if the trinomial can be expressed in the form a² + 2ab + b² or a² - 2ab + b².

Front

Factor the expression: 3x² - 75

Back

3(x + 5)(x - 5)

Front

What does it mean for a number to be a perfect square?

Back

A perfect square is a number that can be expressed as the product of an integer with itself.

Front

Factor the expression: x² - 400

Back

(x - 20)(x + 20)

Front

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

Back

The coefficients must satisfy the relationship 2ab for the middle term, where a and b are the square roots of the first and last terms.

Front

How do you determine if a trinomial is a perfect square?

Back

Check if the first and last terms are perfect squares and if the middle term is twice the product of their square roots.