distrubutive property question?all math geniuses?

Question

do you do distributive property first or combining like terms first?

great answer kyle.as soon as possible i'll give you best answer

what if it was something like this

-8(t/2+6)

Answer 1

If you have a choice, then it doesn't matter. For example:

3(4a + 7a) = 3(11a) = 33a, which is the same as
3*4a + 3*7a = 12a + 21a = 33a.
In fact, combining like terms first gets us to a quicker answer.

Other times, if you have something like 3(4a + 7b), then you can't combine like terms to begin with, so you have to distribute.

Answer 2

Actually, they're both the same thing. Combining like terms is just a special case of the distributive property -- e.g. to say that 5x+3x = 8x is simply abbreviating the deduction 5x+3x = (5+3)x = 8x.

If you're asking whether there's some order of algebraic manipulations akin to the order of operations itself, the answer is no, valid manipulations can be done in any order, as long as the order of operations itself is respected (i.e. don't try to say x+yz = (x+y)z, because it isn't).

Answer 3

Either way gives you the same answer:

Example:
2(4x + 5x)

Dist. property first:
= 8x + 10x
= 18x

Combine like terms first:
= 2(9x)
= 18x


edit:
-8(t/2 + 6)

Since there are no like terms in the parentheses, we distribute first:
= -8*(t/2) + -8*6
= -8t/2 - 48
= -4t - 48

Answer 4

First, use the Distributive Property - then, combine "like" terms. Here is one example...

2(4x+5t) - 7(-10x+8t)

First: eliminate parenthesis - distribute the outer terms with the terms in parenthesis.

2(4x)+2(5t) - 7(-10x)-7(8t)
8x + 10t - (-70x) - (56t)
8x + 10t + 70x - 56t

Sec: combine "like" terms.

8x +70x + 10t - 56t
78x - 46t

Answer 5

it depends on the problem.

example:
3(4x + 5) + 2x; distribute first

3(4x + 5x); you can simplify or distribute first


If there are parentheses, I tell my students that the parentheses are a wall and anything inside the wall can't come out unless the number outside comes to get it, so they have to distribute.