Question

Translate the following phrases into algebraic expressions. Explain, in complete sentences, the difference between the two.
• twice the sum of x and y
• the sum of twice x and y

Answer 1

First one is the same as saying: Multiply the Addition of x and y.

Second one is same as saying: Multiply x by 2 and y by 2 then add the values together.

How can you write that algebraically?

@Tayloresc

Answer 2

x^2 + y^2? @genius12

Answer 3

is x^2 y^2 the same as multiplying the addition of x and y by 2?

Answer 4

Not Quite.

Answer 5

Remember that it says "twice the sum of x and y" so what does "the sum of x and y" mean?

Answer 6

x^2 + y^2

this is : x square plus y square

Answer 7

Exactly ^

Answer 8

So:

Think about this, sum is the same as addition so "the sum of x and y" is?

Answer 9

I'm so confused...

Answer 10

Ok forget about the second question let's focus on the first one:

twice the sum of x and y

Answer 11

so like I said above "sum" is the same as addition so what is the sum of x and y?

Answer 12

xy?

Answer 13

addition : +

Answer 14

not quite, how would you show " Sum of x and y"?

Answer 15

exactly

Answer 16

x + y?

Answer 17

perfect, now the questions says "twice the sum of x + y" so how would you show this?

Answer 18

Keep in mind the distribution process...

Answer 19

I'm not sure

Answer 20

Well how would you multiply x + y by 2?

Answer 21

2(x+y)?

Answer 22

HOORAY :D

Answer 23

Now you know that:

twice the sum of x and y

is the same as

\[2(x+y)\]

Answer 24

Now what is:

the sum of twice x and y

Answer 25

the same thing backwards?

Answer 26

Not quite,

we know that sum is + so....:

twice x + y

Answer 27

2(x+y)

Answer 28

not quite, "twice x + y

Answer 29

The "twice" does not affect the y

Answer 30

(2x)y

Answer 31

Good, but remember it asks for the "sum" of 2x and y not the product (multiplication)

Answer 32

I have to figure out the diffence of the two I don't now what the diffence was

Answer 33

product is the answer to the multiplication problem (1 * 2 = 2)

sum is the answer to an addition problem (1 + 2 = 3)

Answer 34

So:

2x (?) y = [?] (We are solving for "Sum" so it is....)

Answer 35

What?

Answer 36

If we are solving for the sum we must be doing what operation?

Multiplication, addition, subtraction, division?

Answer 37

Sorry I have to go,

@ganeshie8 can you take over?

Answer 38

yea sure :)

Answer 39

I need help I'm clueless

Answer 40

il try

Answer 41

Thnk you

Answer 42

JA1 was explaining fantastic so far !

Answer 43

we know that sum is + so....:

twice x + y

Answer 44

whereever u see 'twice' u can replace it with '2' blindly

Answer 45

twice x + y

2x + y

Answer 46

Done.

Answer 47

still stuck ?

Answer 48

yes

Answer 49

Yes I am @ganeshie8

Answer 50

ok