If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Operations and Algebraic Thinking 222-226>Unit 2

Lesson 2: The distributive property & equivalent expressions

# Factoring with the distributive property

Sal shows how to factor the expression 4x+18 into the expression 2(2x+9). Created by Sal Khan.

## Want to join the conversation?

• how does this help me in real life?
• I'm wondering the same thing, along with quadratic equations, and Pythagorean theorem.
• Can someone tell me what I did wrong here with this equation? The equation is -2(-7k+4)+9=-13 I distributed -2 with -7k and 4 so when I got that I got 14k and -8 so then you put it back in the equation as 14k + -8 +9=-13 right? But then I got stuck with the -8 and 9 I can't figure it out and I have a test on it tomorrow. I need help! I need help with what to do from the step with the -8 and 9. If anyone can figure it out today that would be amazing!! I'm BEGGING YOU
• You just add the -8 and 9. So -8+9=1.
This gives 14k+1=-13. Subtract 1 from both sides to get 14k= -14.
• i dont get it everything doesnt make sense
• i see no real application of this strategy in making toast, taking a shower, or running outside. just sayin. not rlly necessary.
• If you continue to study math, I promise this will be useful! In real life, you might use this if you enter a field in physics, math, engineering, science, or computer science, but for now your main goal in learning this should be to be comfortable with it so you can pick up more difficult math concepts. Starting around Algebra 2 and Precalculus, factoring will become something that needs to come naturally in order to solve more difficult problems.
• For anyone who doesn't understand, its basically undoing the Distributive Property. Instead of Distributing and simplifying, its just figuring out the greatest common factor (GCF) and dividing GCF fro both the numbers.
• how would you do it with negative numbers in the problem
• Same process. Let's factor, say, -8x - 40. So, I can do this in two ways:

1. I can factor out an 8 from both terms. This gives 8(-1x) + 8 (-5). Taking the 8 common, we get 8(-x-5)

2. I can factor out -8 from both terms. This gives -8(x) + (-8)(5). Taking the -8 common, we get -8(x+5)

Both answers are correct, by the way. So, use whichever one you wish to
• Sometimes ours are negative, how can you tell that from a subtraction sign?
• negatives and minuses are the same operation, so it all depends on where it is in the expression or equation. Negatives generally come at the beginning of things (front of expression, front of parentheses, or front of denominator), so in the expression -2(-3)/-6 would all be considered negatives. If it is between things, it is considered as a minus, so 3 - 5 is minus. Then you have the special case of minus a negative such as 4 - (-4) which ends up as a positive 4+4.
• So it's just finding the greatest common factor and splitting the number?
• i dont get it
So lets work on this equation: 10y + 8x
To simplify this equation we have to find a number that both of these numbers can be divided by (AKA finding a common factor). Both of these numbers can be divided by 2, so that will become the number on the outside of the parentheses.
Example:
2(insert number + insert number).
10y divided by 2 is 5y:
2(5y + insert number)
And 8 divided by 2 is 4x"
2(5y + 4x)
You can apply these steps to other equations as well. I hoped this helped and didn't confuse you more!
God Bless!