Solving for the Completely Factored Form of p4 – 16
When it comes to factoring algebraic expressions, it can sometimes be a bit intimidating. But fear not, for we have a handy tool at our disposal: the difference of squares formula. And that’s exactly what we can use to solve for the completely factored form of p4 – 16.
First, let’s refresh our memories on the difference of squares formula. It states that a2 – b2 = (a + b)(a – b). Keep that in mind as we dive into the problem at hand.
We start with the expression p4 – 16. Our goal is to factor this completely, which means we want to express it as a product of two or more factors. We already know that 16 is a perfect square, so we can write it as 42. That gives us p4 – 42.
Now, we can apply the difference of squares formula. In this case, a = p2 and b = 2. So we have:
p4 – 42 = (p2 + 2)(p2 – 2)
And voila! That’s the completely factored form of p4 – 16. It may seem like a small victory, but mastering these little techniques is what helps us tackle more complex problems down the line.
Of course, factoring is just one small corner of algebraic problem solving. But with tools like the difference of squares formula and a bit of practice, you’ll be able to tackle more and more challenging equations with ease. Happy solving!