This week we completed the polynomial unit and had our unit test, but we still learned a couple of things, one of which was difference of squares.
Let’s say we have the binomial , 16 is a perfect square (4×4). We can use this information to break it down or “factor” it. The x is squared, so this means it can be broken in half. So now we know that both parts of the binomial can be broken in half, but there is one problem, the 16 is negative. A negative and a negative equals a positive, and a positive and a positive make the same, so one of the 4’s in 16 will have to be negative.
The resulting factored polynomial is: (or vice versa).
But what if the binomial has a variable that is not squared but with an exponent of 4, 6, 8? As long as the variable has an exponent that is even, and the other term is a perfect square, you can use a difference of squares.