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# algebraic expressions

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Consider the expression: 5(3x + 3) + 2(3x - 2).

Use the distributive property to simplify and create an equivalent expression.

Mar 16, 2021

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i'm not really sure how to explain how to do this... but when you expand, you just multiply the factors from left to right.

so, using the distributive property, let's expand the first expression:

5(3x + 3) = 5(3x) + 5(3) = 15x + 15. hopefully you can follow what i did there.

now, using the same process, let's expand the other expression.

2(3x - 2) = 2(3x) - 2(2) = 6x - 4.

now, here is the expression we have currently:

15x + 15 + 6x - 4

to simplify, we combine the like terms and constants.

(15x + 6x) + (15 - 4) = 21x + 11

hope this helped! by the way, here is a site that may explain using the distributive property clearer:

https://www.prodigygame.com/main-en/blog/distributive-property/#:~:text=Distributive%20property%20with%20exponents%201%20Expand%20the%20equation.,4%20Solve%20the%20equation%20and%20simplify%2C%20if%20needed.

some expanding calculators are also helpful. they can help you explain step-by-step as well. i recommend using Symbolab, SoluMaths, or MathPapa (these will work for most of the simpler expansions).

i also struggled with this when i was younger... so here are some more generic expansions

\(a(b+c) = a(b) + a(c)\)

\(a(b-c) = a(b) - a(c) \)

\(a(-b-c) = a(-b) - a(c)\)

there are probably more, but i hope you get the general idea! i recommend that you try and memorize some of these, or at least understand the patterns / logic.

i truly hope you can use some of these tips / resources that i have provided above. if you have any further questions, feel free to ask! :)

Mar 16, 2021