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Lesson 12: Distributive property with variables

# Distributive property with variables

To apply the distributive property to an algebraic expression, you multiply each term inside the parentheses by the number or variable outside the parentheses. For example, to simplify 2(x + 3), you would multiply 2 by both x and 3, resulting in 2x + 6.

## Want to join the conversation?

• At , how does 1/2 (2a) just equal to a? Shouldn't it be 1?
• Basically, when you multiply 1/2 with 2a, you get 2/2a. 2/2a equals to 1a, which is equal to a
• This is still super difficult.
• true that, Still confuzzled
• Bruh moment, pls help, confuzled tots
• Yesssss! i like the rhymes but what do you need help on is what confuses me
• What is happening i'm so confused!
• yea, But like everything, you will get good.
• i dont get this question
6(5x -3)=
• Just use the distributive property, that is, multiply the number outside the parantheses and the number inside the parantheses.
In this case,
6 (5x-3)
= 6 ·5x - 6 ·3
= 30x - 18.
• How to factor using the distributive property?
• Factoring is essentially the reverse process. In a expression, factoring is bringing out as many common factors out as possible from it. Common factors are factors shared by all terms in the expression.
When you have obtained your factored form, you can verify that it is correct by expanding it out using the distributive property as we have learned.

To illustrate, with the distributive property itself: `a(b+c) = ab + ac`
If we had `ab + ac`, this can be factored because `a` is a common factor of both the terms, thus becoming `a(b+c)`.

Eg. Factor `4x^2 + 2x`
`4x^2` and `2x` both share `x` as a common factor. But the coefficients of `4` and `2`: they share `2` as a common factor. In total, `x*2` or `2x` can be factored out from `4x^2 + 2x` like so:
`4x^2 + 2x = 2x(2x + 1)`
We can verify this like so:
`2x(2x + 1) = 2x*2x + 2x*1 = 4x^2 + 2x`

Hope this helps anyone
(1 vote)
• how does 2a turn into q if 6b turns into 3b why didn't 2a turn into 1a? plz help!
• Woah - it wasn't a `q`, it was an `a`!
`6b` turned into `3b` as usual, because `6/2 = 3`.
`2a` turned into `a`. `2/2 = 1`. Technically it becomes `1a`, but `1*anything = anything` so we don't have to write down that `1`.
In short, `1/2*(6b + 2a) = 3b + a`.

Hope it helped.
• can someone please tell me where i have to go to understand how to solve 11(6+3h)
• ok so
11(6+3h)
you have to distribute because its distribute property
11 times 6 = 66
11 times 3h = 33h
so the answer is 66+33h (because you cant add unlike variables)hoped that helped