## anonymous one year ago Two sets of equatic expressions are shown below in various forms: Line 1: x^2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)^2 − 0.25 Line 2: x^2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)^2 + 6.25 Which line contains three equivalent expressions?

1. anonymous

line 1 only line 2 only line 1 and line 2 neither line 1 or lime 2

2. anonymous

@myininaya

3. johnweldon1993

Do you know how to distribute out the parenthesis? e.g) (x+1)(x+2)

4. anonymous

I think so don't you use FOIL? @johnweldon1993

5. johnweldon1993

Yes use foil to distribute those out..in both cases

6. anonymous

line 1 x^2 +2x+x+2 line 2 x^2+3x+2x+6 is that correct @johnweldon1993

7. johnweldon1993

yes...now just combine like terms...and we have line 1) x^2 + 3x + 2 line 2) x^2 + 5x + 6 So far those match the first part of each line...so we move onto the next part as well So now we need to distribute the line 1) (x + 1.5)^2 - 0.25 line 2) (x + 2.5)^2 + 6.25

8. anonymous

then it would be x^2 +1.5^2-0.25 x^2+2.5^2+6.25

9. anonymous

@johnweldon1993

10. johnweldon1993

Ahh not quite :) So think of something like $\large (x + a)^2 \rightarrow (x + a)(x + a)$

11. anonymous

oo so it would be (x+1.5)(x+1.5)-0.25 (x+2.5)(x+2.5)+6.25 @johnweldon1993

12. johnweldon1993

Correct....so you foil those parenthesis out and then just simplify :)

13. anonymous

the first one should be x^2+3x+2

14. anonymous

the second one should be x^2+5x+12.5

15. johnweldon1993

Perfect....so as you can see...line 1 is the same...but line 2 is no longer the same..thus the answer is...?

16. anonymous

line 1 only @johnweldon1993

17. johnweldon1993

There we go :)

18. anonymous

thank you so much @johnweldon1993