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### Course: Algebra 1>Unit 13

Lesson 2: Multiplying binomials

# Multiplying binomials intro

Sal expresses (x-4)(x+7) as the standard trinomial x²+3x-28 and discusses how the general product (x+a)(x+b) can be written as x²+(a+b)x+a*b.

## Want to join the conversation?

• What are your guys reasons for doing khan?
• dopamine hit from getting all questions correct
• At he said "standard Quadratic form". Previously he spoke about standard from and just said you order in from greatest degree to lowest degree and didn't mention the Quadratic part, is standard Quadratic form more specific?? And what does the 'Quadratic' part explain?
• He's just specifying the type of equation he's working with.

Extra info: There are four specific ways to reference the degree (the greatest exponent) of an expression:

Linear: degree of 1; (x+2),(x)
Quadratic: degree of 2; (x^2-5x+2),(x^2+3),(x^2+8x),(x^2)
Cubic: degree of 3; (x^3+x^2+x+1)
Quartic: degree of 4; (x^4)
It doesn't matter how many terms are in an expression when you're trying to determine its degree.

Information related to the kind of examples given: The number of terms in an expression has three specific words, and one general word.

Monomial: Only one term
Binomial: Two terms
Trinomial: Three terms
Polynomial (general): More than three terms
• Why plus seven at the start?
• I think the idea was that you take the two terms, here being x and positive 7 and distributing each term to (x-4) and once you get the binomial products, you add them together to get the answer of x^2+3x-28. Another method to multiply binomials is FOIL or First Outside Inside Last. Both of these methods will give you the same answers but FOIL is typically faster. Hope this helps!
• What's the "FOIL" method that everyone in the comments is talking about?
(1 vote)
• FOIL stands for First Outside Inside Last. It's a mnemonic for multiplying two binomials, and here's how it works!
Let's say we have the expression (2+4)(7-5).
We start by multiplying the first terms:
2*7
Then we add the product of the inside (or closest to the middle) terms:
2*7 + 4*7
Next we add the product of the outside terms
2*7 + 4*7+ 2*-5
And finally, we add the product of the last terms.
2*7 + 4*7 + 2*-5 + 4*-5

Now we solve it. It's not necessary, but it is a little easier to solve if we put parentheses in:
(2*7)+(4*7)+(2*-5)+(4*-5)
Which becomes
14 + 28 + (-10) + (-20)
42-30
=12

And that's FOIL!

Edit: ACK! I messed up the order of the instructions. (I gave you FIOL instead of FOIL!) But it doesn’t really matter which order you do it in as long as you keep track of your terms. So if you want to do it the official way (for example, if you have to show your work) just switch Inside and Outside in my instructions. Sorrrrrryyyyyyyyyyyy 😅🙇🏻‍♀️
• The general product can be written as shown above because he is basically taking steps instead of doing it at once .
• Doesn't FOIL seems easier and it takes fewer steps? To me it does.
• Foil is often easier for multiplying two binomials, but you need other methods later on to do trinomials by binomials or trinomials by trinomials.
• in an exam do i have to write every step?
cuz this is how i do it
(x-4)(x+7)
x^2+7x-4x-28
(1 vote)
• Most teachers ask you to show your work so if you make an error they can help you understand it and correct it. But, you need to ask your teacher what they require.
• What's the "FOIL" method?