[Math10] What I learned this week (Nov 4th)!

This week, I learned how to use a new method to use the distributive property called (FOIL)! Here’s how:

First - Multiply the first term in each set of parentheses
Outer - Multiply the outer term in each set of parentheses
Inner - Multiply the inner term in each set of parentheses
Last  - Multiply the last term in each set of parentheses

Example 1: (3 + 7x)(6 + 2x)

the first thing we need to know is how we use FOIL! FOIL is the same thing as using the distributive property, however we are using a binomial to distribute like this:

foil1

Looks familiar? That’s because you do the same step using a monomial! Were basically doing the distributive property… twice! So let’s go through this, first distributing using the 3:

foil2

Great, now let’s do it with 7x:

foil3

 

Finally we can simplify this answer! We don’t need both 6x and 42x, so we just add them together, the answer is 48x! Now we have our final answer: 18 + 48x + 14x^2

Example 2 (x^2 – 4)(2x^3 + x – 5):

This one is where is gets complicated! First, let’s use FOIL:

foil4

Alright, let’s begin by distributing the x^2:

foil5

Next let’s distribute -4:

foil6

 

Wow, that’s a lot of numbers! Now we just have to simplify: The only thing we can simplify is x^3 and -8x^3

The final answer is 2x^5 + -7x^3 – 5x^2 – -420

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