Question

Two sets of equatic expressions are shown below in various forms:

Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25
Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25

Which line contains three equivalent expressions?

Answer 1

Please help

Answer 2

What does "equivalent expression" mean to you? How do you recognize an "equivalent expression?"

Answer 3

it means the expressions have the same answer

Answer 4

(equivalent answers)

Answer 5

Not quite. expressions don't have "answers."
What have you done so far? What could you do to each expression to give it just one format that you can easily compare?

Answer 6

factor them?

Answer 7

"answer" isn't applicable here. It's "equivalence" that's important.

Have you tried factoring any of the given expressions?

Answer 8

yeah

Answer 9

I'd like to see your results. Please share whatever you've done so far.

Answer 10

first one is (x+1)(x+2)

Answer 11

Simplify as much as possible, and factor: (x + 1.5)2 − 0.25

Answer 12

its (x+2)(x+1)

Answer 13

or (x + 1)(x + 2)

Answer 14

Note: by (x+1.5)2 you probably meant\[(x+1)^{2}\]

Answer 15

no i think your wrong on this 1

Answer 16

Yes, I'm wrong. Show me all of your own work.

Answer 17

if you factor (x + 1.5)2 − 0.25 it will give you (x + 1)(x + 2)

Answer 18

Expand (x+1.5)^2.

Answer 19

ok

Answer 20

wait expand???

Answer 21

That (x + 1.5) is a binomial.

You are asked to find the square of this binomial.

That means multiplying out (x+1.5)(x+1.5). That's what I meant by "expansion"

Answer 22

Expand:\[(x+1.5)^2\]

Answer 23

(x+1.5)(x+1.5)
=(x+1.5)(x+1.5)
=(x)(x)+(x)(1.5)+(1.5)(x)+(1.5)(1.5)
=x2+1.5x+1.5x+2.25
=x2+3x+2.25

Answer 24

there

Answer 25

Good. Please, indicate exponentiation with the ^ symbol.

(x+1.5)^2, not (x+1.5)2.

Answer 26

k

Answer 27

Now, subtract .25 from your result. What do you get?

Answer 28

x2+3x+2.25−0.25
=x2+3x+2.25+−0.25
Combine Like Terms:
=x2+3x+2.25+−0.25
=(x2)+(3x)+(2.25+−0.25)
=x2+3x+2
Answer:
=x2+3x+2

Answer 29

Good. Now, factor that.

Answer 30

k

Answer 31

(x+1)(x+2)

Answer 32

just like my first answer

Answer 33

Look at the given expressions, first row. Is your most recent result the same as the middle expression in the first row?

Answer 34

yes

Answer 35

i know that

Answer 36

great. So, we call the 2nd and 3rd expressions in the first row " ? "

Answer 37

so line 1 is a "equivalent expression"

Answer 38

now we need to find out about line 2

Answer 39

Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25

Answer 40

We haven't looked at the first expression in line 1 yet. but "equivalent" was properly applied here.

Are all 3 expressions in Line 1 equivalent? yes or no

Answer 41

yes

Answer 42

So, Line 1 could be the line y ou were looking for, with all 3 expressions "equivalent."

Answer 43

all of then are (x+1)(x+2)

Answer 44

but we need to find out if line 2 is or not

Answer 45

Please re-write (x + 2.5)2 + 6.25 using the proper symbol for exponentiation.

Answer 46

ok

Answer 47

x2+5x+12.5

Answer 48

??? Where is your " ^ " symbol, to express exponentiation?
Where did that 12.5 come from?

Answer 49

nvm ur no help

Answer 50

I'm making sure you understand the concepts involved. Sorry that you don't want to take this to completion, especially since we're so close to finishing.

Answer 51

Please re-write (x + 2.5)2 + 6.25 using ^ for exponentiation, and explain how you got 12.5.