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### Course: Algebra basics>Unit 7

Lesson 2: Multiplying binomials

# Multiplying binomials: area model

Sal expresses the area of a rectangle whose height is x+2 and width is x+3.

## Want to join the conversation?

• why do I have to do math.

Math is good for your brain! It makes you smarter (insert sarcasm: wow really? I didn't know that), and improves your problem solving abilities.

When you become an adult, you'll have to manage money. Doing that requires a lot of math. Even just going to the grocery store and shopping smart takes basic arithmetic (and basic algebra if you want to be meticulously thorough).

Math helps you understand the world! This is why I really like math (note: I like math as a concept. Calculations are boring :P) Everything around you. Every tree, flower, bookcase, speck of dust, it has math woven into it's being. As Galileo said, "The universe is a book, and math is the language it's written in." Now admittedly, the math you're learning right now is kind of boring, but if you stick with it, you'll be able to learn some really cool concepts!

If you don't want to stick with it, and just want some simple math awesomeness, there's a youtuber I really like, ViHart, that explains some really fun mathematical concepts without using numbers! If you're interested, I highly recommend checking it out.

Anyway, that answer was really cheesy, and you've probably heard it a million times already, but yeah. Math is fun, but it can get REALLY annoying sometimes, especially when you're trying to learn this thing, and the thing makes no sense, and the thing is stupid an you're like "I DON'T WANT TO LEARN THIS THING." I've been there. Many times. But you'll get through it :)
• so frustrating with 9th grade math (╯▔皿▔)╯
• i'm not even in the equivalent of 9th grade and I have to do this lol
• At why can you combine 3x and 2x into 5x, but you can't combine x-squared with those?
• because you don't know what x is, so you assume x is not equal to x^2
• You can just factor out the binomials using the FOIL method right?
• Yes, you can multiply the binomials using FOIL method.
Factoring is the opposite of multiplying.
If I multiply 3 and 5 then I get 15.
If I factor 15, then I get the factors 3 and 5, or 1 and 15.
Hope this helps.
• is this important
• Yes. Our infrastructure is built on math.
• but... but... this is a parabola! how come the area of this squares combined can be equle to n ENDLESS line that only intersects the x line 2 times? this is INSANITY!
• I think you are saying that the equation he ends up with could also be the equation defining a parabola, correct? Well, that might not be quite so strange as you think. You see, x is a variable, so we do not know its value. Depending on the value of x, the area of the square will be different. You could make a graph using different x values in this equation, and the y values you come up with will be the area of the square corresponding with different x values. What's more, if you plot the points (the x values and the area values that go with them), you will create a parabola!

I am so glad you mentioned this because I would not have otherwise thought about this interesting relationship. Math is so amazing, isn't it?

(The negative values wouldn't really make sense for length and area, though.)
• how is this gonna help me in life and prepare me for the future
• jobs in astronomy require some advanced knowledge in math to apply
• Hey Khan Academy, I'm a bit confused with a multiplying binomials question I got wrong on a quiz.

I was under the impression, based on Sal's multiplying binomials videos, that if you were to multiply a binomial such as: (a+7y)(9y-12a) that you can distribute the second binomial to the first binomial: 9y(a+7y)-12a(a+7y) and solve.

That's how I've been approaching the multiplication of binomials and I've been getting the correct answers.

The question on the quiz distributred the first binomial to the second, so the reverse order to what I thought Sal was instructing us to do.

Any clarity you can provide would be much appreciated!

Thanks,
• Both ways are correct, whether you start from the first binomial or the second binomial, you still end up with the same answer.

To prove:
(x+2)(x-3)
Can be written as:
x(x-3)+2(x-3)
x²-3x+2x-6
x²-x-6
Can also be written as:
x(x+2)-3(x+2)
x²+2x-3x-6
x²-x-6