Distributive property and Factoring completely (algebra)

Basic algebra flashcard for the basics on distributive property, factoring out (look at my acc for factoring out), and how to use it on polynomials.

What does distributive property allow you to do?

You can take a factor and distribute it to each member if a group of things (if their being subtracted or added) and still get the same answer. Ex: 2(3+4) gives you the same answer as 2×3+2×4

What is the formula that represents distributive property?

a(b+c)=ab+ac

Does distributive property work on + and -

Yes

Does distributive property work on x and ÷ ?

no (except x in a term)

What does distributive property look like on

2x(6-8) ?

12x-16x

Solve 8(5+3) using distributive property

64

Simplfy 3(x+6) using distributive property

3x+18

Does distributive property still work on terms, since their already being multiplied?

Yes, when using distributive property on a term treat each term as a member of the group (equation),

Use distributive property on 2(x+y+z)

2x+2y+2z

Simplfy using distributive property on 10(a-b+4)

10a-10b+40

Simplfy using distributive property on 2(g+h+6)

2g+2h+12

Does distributive property work on a variable or integer with a exponent?

Yes, just add onto the exponent

Simplfy 2(3x+5y) using distributive property

You are able to multiply the number part in a term:

6x+10y

Simplify 4(x²+3x-5) using distributive property

4x²+12x-20

Simplfy x(x²-3x+2) using distributive property

x³-3x²+2x

Does distributive property work in reverse?

Yes and we call in factoring out

Can you multiply with a varible using distributive property? And what happens when you use it on another varible?

Yes you can use distributive property with a varible: x(2+3)=2x+3x. When multiplying a varible with a varible since it would look like this; x·x, we can simplfy it to x². x(x+4)= x²+4x

How do you factor out and how does it work?

Factoring out means taking the factor (ex: 2 Is a factor of 6 since 2×3=6) of a set of numbers,then basically dividing them by it so you can multiply the set as a whole by that factor.

Why can you factor out on 6×9×12?

Because they are all factors of 3, (3×2=6)

thus 3(2+3+4)=6×9×12

Factor out 10a+15b+20c

5(2a+3b+4c)

Factor out x²+6x-23x

x(x+6-23)

Factor out 8x+6x+4z than use distributive property on it

—> 2(4x+3x+2z) —> 8x+6x+4z

Factor out 6x⁴-8x²-10x⁶

2x²(3x²-4-5x⁴)

Factor out 4x+80x-20x⁵

4x(20-5x⁴)

Factor out ax²+ax+a

a(x²+x+1)

*You can replace it with 1 because the value will not change.