Question

Simplification of polynomial expressions: need step by step so that I can teach my son. Specifically two forms: -3(2x-5)-1, and -6v-2(4-7v). All I have to go on atm are dim memories from 30 years ago. Please help.

Answer 1

Here you need to use the distributive property of multiplication over addition. What that long name means is simply this: when you multiply a number by a sum inside parentheses, you _distribute_ the number by what is inside the parentheses.
Example:
5(2 + 3) = 5 x 2 + 5 x 3 = 10 + 15 = 25
Notice that if you had done this using the normal order of operations, which is to do what's inside the parenthses first, you'd get
5(2 + 3) = 5(5) = 25
You get the same result as by distributing the 5 above.

Answer 2

So each factor outside by each factor inside is the way to go? For both examples or just the 1st?

Answer 3

and there are invisible parentheses, i am assuming, : (5x2) + (5x3).

Answer 4

And does the FOIL method come into play on the second, because I keep getting different answers, and none of them are 8v-8, as another site says.

Answer 5

Let's start with the first problem:
-3(2x - 5) -1
Be careful with the negative number outside the parentheses
= (-3)(2x) - (-3)(5) - 1

Answer 6

Now we multiply the numbers together:
-6x + 15 - 1
Now combine like terms:
-6x + 14

Answer 7

or divide by 2?

Answer 8

Now for number 2. BTW, FOIL if for this situation: (2x + 5)(3x - 6), for example. It's the multiplication of two binomials. In this case you are not doing that either with the first or second problem.

Answer 9

ok got it.

Answer 10

The second example from your post now:
-6v - 2(4 - 7v)
First term reamis the same because the first thig to do is the parentheses. So start by distributing the -2
- 6v - (2)(4) - (2)(-7v)
-6v - 8 + 14v
8v - 8

Answer 11

pemdas

Answer 12

Right, that's why after we do the distributing, we do the multiplications first and then additions and subtractions.

Answer 13

and you need do nothing with the 8 to make it smaller? And I notice that there's a factor left out, -1 and -6v, respectively, in each. Is that always the case?

Answer 14

These two problems are just simplifying expressions. The first one had the -1 at the end which did get used by combining it with the 15 from the distribution. In the second problem, the -6v combined with the +14v to give 8v

Answer 15

Just wondering if you are going to have to set aside and bring back numbers every time? I understand the results and how we arrived at them.

Answer 16

If the problem were simply 2(x + 8), then there's only a distrubition to do:
(2)(x) + (2)(8) =
2x + 16
There are no extra numbers to combine.

In the two specific problems you posted there were extra numbers beside the part of distributing, that's why we had to distriburte first and tnen combine the extra numbers, the -1 in the first problem and the -6v in the second one.

Answer 17

That was the exact notion that I was stumbling over when trying to explain this to my son. Thanks. You are a deity of order and calculation. ;p I may be back to bother you soon.

Answer 18

any time, as long as I'm online

Answer 19

I'll leave you alone at home, then... good night.