Grade 9 Algebra: Please Help! Multiply Polynomial Expressions

Question

Direction: Select a set of expressions above (Set A, Set B, or Set C) to focus on for the questions below.

( I chose set B )

Set B

(x+5)(x+5)

(2x+9)(2x+9)

(x+1)²

1. Identify which set of expressions you selected.
2. Describe how to multiply these expressions.
3. Find the products of the three problems in your chosen set.
4. Give a NEW example of a multiplication problem that could be added to your set based on its structure. Find the product of your created problem.
5. Give an example of a multiplication problem that would NOT be included in your set based on its structure. Explain why this problem would not be included in your set.

Answer 1

The factors of the expressions you picked (such as "x + 5" are called binomials because they each have 2 terms in them (in this case "x" and "5"). There are several tools you can use to multiply two binomials.

You can just use distribution but you must distribute every term in one binomial to every term in the other like this:

So the answer is x² + 10x + 25 (because 5x + 5x = 10x).

However, this can be a little confusing. To help, someone came up with the acronym "FOIL" where each letter tells you what to multiply. "F" means multiply the two "First" terms (x • x = x²), "O" means multiply the two "Outside" terms (x • 5 = 5x), "I" means multiply the two "Inside" terms (5 • x = 5x) and "L" means multiply the two "Last" terms (5 • 5 = 25).

Do the other problems just like this. Before you do the last problem, rewrite it as (x + 1)(x + 1).

Notice that this FOIL method will not work if there are three (or more) terms in either one (or both) of the factors. So, an example that would NOT work using the FOIL method is (x + 2)(2x² + 3x + 5)