Combining like terms

[Dillinger4]

Ive been having trouble understanding how to combine like terms when multiplication is distributed over addition. If anyone could help it would be great. Two problems that i have banging my head over are the following

4(2x³ + x²) - 5x²
= 8x³ - x² 'books answer

I end up getting 8x³ + 4x² - 5x²


Here is another one..... 3(5c) - 15c² + c
-15c² + 16c 'books answer

Now 3 * 5c would give us 15c.

15c - 15c² or 15c + (-15c²)

should gives us 0 c¹ which boils down to c

so i end up with c + c.

[NotLKH]

Thats Puzzling!

[Dillinger4]

Im puzzled by what you find puzzling

[thinktank2]

Originally posted by Dilenger4
Ive been having trouble understanding how to combine like terms when multiplication is distributed over addition. If anyone could help it would be great. Two problems that i have banging my head over are the following

4(2x³ + x²) - 5x²
= 8x³ - x² 'books answer

I end up getting 8x³ + 4x² - 5x²


Here is another one..... 3(5c) - 15c² + c
-15c² + 16c 'books answer

Now 3 * 5c would give us 15c.

15c - 15c² or 15c + (-15c²)

should gives us 0 c¹ which boils down to c

so i end up with c + c.

I don't know whether you are just joking are not..
But anyway..

1) 4(2x^3 + x^2) - 5x^2

= [(4*2)*x^3] + [4*x^2] - [5*x^2]

= 8x^3 + [4-5](x^2)

= 8x^3 + (-1 * x^2)

= 8x^3 - x^2

2) 3(5c) - 15c^2 + c

= 15*c - 15c^2 + 1*c

= [15 + 1]*c - 15c^2

= 16c - 15c^2

= -15c^2 + 16c

[Dillinger4]

Thanks thinktank2. I kind of understand your break down of the second problem.

2) 3(5c) - 15c^2 + c

= 15*c - 15c^2 + 1*c

= [15 + 1]*c - 15c^2

= 16c - 15c^2

= -15c^2 + 16c

3(5c) - 15c² + c
-15c² + 16c

But why would 3(5c) + c = 16c? wouldn't it be 15c²

[Ambivalentiowa]

About the first one:

Originally posted by Dilenger4

4(2x³ + x²) - 5x²
= 8x³ - x² 'books answer

I end up getting 8x³ + 4x² - 5x²

8x³ - x² = 8x³ + 4x² - 5x²


For the second one:

3(5c) = 15c
15c+c = 16c
15c(c) = 15c^2

[NotLKH]

Originally posted by Dilenger4

But why would 3(5c) + c = 16c? wouldn't it be 15c²

It is, when c = 0, or c = 16/15

[[Digital-X-Treme]]

Text books don't always show the right answers...

[Ambivalentiowa]

Except that in this case they have so there's not a problem there.

[Dillinger4]

Posted by Ambivalentiowa
8x3 - x2 = 8x3 + 4x2 - 5x2

So if they are equivalent then i guess i had the answer right to begin with? Thanks guys.

[Dillinger4]

Here is another one that i find hard.

6[5c + 4(d-2c)] -5c

Now i assume that i should start with the inner most grouping.

6[5c + 4d - 8c] - 5c

Now i guess i have to use the distributive property as such. But im not sure if im doing this right.

30c + 24d - 48c - 30c

Now since the answer is supposed to be -23c + 24d i can see where 24d comes from but where does the -23c come from?
30c + -48c = -18 and -18 + (-30c) = -48c.

So i end up getting -48c + 24d

[Ambivalentiowa]

Originally posted by Dilenger4
Here is another one that i find hard.

6[5c + 4(d-2c)] -5c

Now since the answer is supposed to be -23c + 24d i can see where 24d comes from but where does the -23c come from?
30c + -48c = -18 and -18 + (-30c) = -48c.

So i end up getting -48c + 24d

6[5c+4(d-2c)]-5c
6[5c+4d-8c]-5c
6[4d-3c]-5c
24d-18c-5c
=24d-23c

You seem to have multiplied the -5c by 6 which is incorrect to do.

[da_silvy]

JUST having a shot, seeing if i can still do it

6[5c + 4(d-2c)] -5c
= 30c + 24(d-2c) - 5c
= 25c + 24d - 48c
= -23c + 24d
or
= 24d - 23c



lol

[Ambivalentiowa]

Very good da_silvy.

[Dillinger4]

Ahhhh ok. We start from the outer and work our way towards the inner.

[Ambivalentiowa]

Got any other problems? I'm better at maths than vb.

[da_silvy]

hehehe thanks ambiva

Dilenger, it's really just a matter of personal preference.

For this problem, i just multiplied the six out first, ambiva multiplied out the internal one first. We both got the same answer

[Dillinger4]

Posted by da_silvy
Dilenger, it's really just a matter of personal preference.

For this problem, i just multiplied the six out first, ambiva multiplied out the internal one first. We both got the same answer

Ahhhh ok, i see now. Either way it works out the same.

6[5c + 4(d -2c)] - 5c
6[5c + 4d - 8c] - 5c
30c + 24d - 48c - 5c
-23c + 24d

Thanks for the help guys.

[Ambivalentiowa]

You're welcome.