How do you factor the difference of the two squares? How do you factor the perfect square trinomial?
How do you factor the same and difference of two cubes?
Which of these tree makes the most sense to you?
they all make sense to me.
Review the topic in your text, where all are explained just as well as any of us here could do so.
Where do you have trouble?
To factor the difference of two squares, you can use the identity: a² - b² = (a + b)(a - b). This formula can be applied when you have two terms squared with a subtraction sign between them. For example, if you have x² - y², you can factor it as (x + y)(x - y).
To factor a perfect square trinomial, you need to identify it as one. A perfect square trinomial is of the form a² + 2ab + b² or a² - 2ab + b², where both the first and last terms are squares, and the middle term is twice the product of the square roots of the first and last terms.
For example, if you have x² + 4x + 4, you can factor it as (x + 2)(x + 2), or simply (x + 2)².
To factor the sum and difference of two cubes, you can use the following formulas:
(a³ + b³) = (a + b)(a² - ab + b²)
(a³ - b³) = (a - b)(a² + ab + b²)
Here, both the sum and difference of cubes have a similar form with one cube raised to a power and the other cube raised to the same power but with an opposite sign. Notice the patterns in the factors: the first term in the factor is the same as the first term in the expression, the second term in the factor is the opposite of the second term in the expression, and the last term in the factor is the square of both the first term in the expression and the second term in the factor.
As for which concept makes the most sense, it ultimately depends on your understanding and familiarity with each concept. All three methods for factoring have their own unique patterns and formulas. It's important to practice each method to increase your proficiency in factoring and determine which one you find most intuitive and helpful for different types of problems.