12a(a+b)(a-b)?

Question

please explain what you are doing so that i can understand how you got the answer

Answer 1

you multiply everything out using the distributive property, but first you have to get rid of the parenthesis.
(a+b)(a-b)=a^2-b^2
and now, you have
12a (a^2 - b^2)
When you multiply exponents with the same base, you add the number of the exponents. so for example, if you have 5 to the 3rd power times 5 to the 2nd power, you'd get 5 to the (3+2), or 5 to the fifth power.
same thing, when you multiply "a" and "a" squared, you have "a" to the 3rd.
so when you multiply the parenthesis all out, you get
12a^3-12ab^2
*hope that wasn't too confusing~

Answer 2

Well, (a+b)(a-b) is a special situation which you should remember for life being a^2 - b^2 [(a+b)(a-b) being (a*a + a*-b + b*a + b*-b) being (a^2 - ab + ba - b^2) being (a^2 -ab +ab - b^2) resulting in (a^2 - b^2)
a^2 meaning a-square
Now, we've got: 12a(a^2 - b^2) resulting in 12a*a^2 - 12a*b^2 equalling 12a^3 - 12ab^2.
Absolutely usesless of course, but a good brain excersise. Thanks!
If you did not get the beginning (a+b)(a-b) you work out like (a+b)(c-d) -> (a*c + a*-d + b*c + b*-d) -> (ac - ad + bc - bd)

Answer 3

12a(a+b)(a-b) - Original problem

12a(a^2+ab-ab-b^2) - FOIL (multiply first terms of each parenthical expression, then the "outside terms" or the first and last, the "inside terms" or the second and third, and the last terms)

12a(a^2-b^2) - Simplify (ab-ab=0)

12a^3-12ab^2 - Simplify (12a x a^2 = 12a^3, 12a x b^2 = 12ab^2)

Good luck! Email me if you need more help at [e-mail]

Answer 4

use the FOIL method on (a+b)(a-b). If you don't know, FOIL means first, outside, inside, last. That should give you: a^2 + b^2
then multiply that by 12a to get 12a^3 + 12ab^2. I think that's right---I haven't done algebra in about 10 years, so I may be mistaken. Hope that helps.

Answer 5

12a(a+b)(a-b)

If you are confused do it part by part
First I only multiplied the first part.
= (12a^2 + 12 ab ) (a-b)

= 12a^3 -12a^2b . . . .<> 12a^2b -12ab^2

= 12a^3 -12a^2b + 12a^2b -12ab^2 (the middle two cancel out)

=12a^3 -12ab^2


Note
a^2 = a squared
a^3 = a cubed

Answer 6

12a(a+b) (a-b)
=12asquared +12ab (a+-b)
You cannot simplify further since they’re not like terms. :)

Distribute 12a through the first set of parenthasis (12a x a = 12a squared, then 12a x b = 12ab)
and that's about all you can do.

Answer 7

(a+b)(a-b) is a difference of two squares. it multiples out to a^2-b^2

so 12a(a+b)(a-b)
= 12a(a^2-b^2)
=12a^3 - 12ab^2 (multiply both terms by 12a)

Answer 8

You know, that (a+b)(a-b) is always (a^2-b^2)?

So next step:

12a(a^2-b^2) = 12a^3 - 12ab^2

Answer 9

=(12a^2+12ab)(a-b)
=(12a^3-12a^2+12a^2b-12ab^2)
=12a^3-12ab^2

it is just the distubtive property where you mulitply everything out

there is a shortcut to if you know that (a+b)(a-b) will turn out to be (a^2-b^2) you can say

=12a(a+b)(a-b)
=12a(a^2-b^2)
=12a^3-12ab^2

Answer 10

first, multiply (a+b) and (a-b) by taking each variable in the first and multiplying it by each variable in the second:
12a(a^2-ab+ab-b^2)

next, -ab and +ab cancel each other out, so you get:
12a(a^2-b^2)

next, multiply by 12a:
12a^3-12ab^2