This week we finished our radical unit and began our polynomials unit. Although we only had two days of lessons, I learned a new trick when solving polynomial expression. It involves substituting parts of the trinomial with variables.
When first looking at our polynomial expression, we will notice that it is somewhat of an ugly expression. The trick to make it look nicer is to replace each binomial within the brackets with a variable. So, for this expression we will replace 7x + 2 with the variable a and 4y – 1 with the variable b. Next, we can right it out like (a + b) (a – b) which is the same as you would write it had the binomials been there. Now that we can see the visual of what it will look like, we can replace the variables with their original binomials which will give us (7x + 2 + (4y – 1)) (7x +2 – (4y – 1)). Next, we can foil out our numbers to get the answer to this polynomial expression which will give us the final answer of (7x + 4y + 1) (7x – 4y + 3). This helpful trick makes it easier to solve this expression without working too hard, it is much easier and faster than keeping the original binomials.