(1) ExPAND ThE PoWERS

To expand , you can use the binomial theorem, which states that . In this case, , , and . This gives you:

Calculating the coefficients and powers, you get:

This simplifies to:

So, .

The expansion not only helps us understand the polynomial better, but it can also be a stepping stone for calculating limits, finding roots, or even in applications like curve sketching. Breaking a polynomial down makes it much easier to analyze!

When expanding, it’s common to make mistakes with the signs, especially with negative numbers. One classic pitfall is miscalculating the powers of negative signs, which can lead to incorrect coefficients. Always double-check the binomial coefficients and the powers to ensure everything matches!