Two sets of quadratic 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?

Question

Two sets of quadratic 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?

mathstudent55 · Answer

Start with line 1.
We have x^2 + 3x + 2
Can you multiply out (x + 1)(x + 2) to see if it equal to x^2 + 3x + 2? (Use FOIL.)

anonymous · Answer

Yes it is equal @mathstudent55

mathstudent55 · Answer

Good. Now we need to see if the next expression is also equal.
What is $(x + 1.5)^2 − 0.25$ equal to?
First, square the binomial. then subtract 0.25 from it. What do you get?

anonymous · Answer

Yeah its equal you get the original equation.,

mathstudent55 · Answer

Correct. So line 1 is the answer. All three expressions are equivalent.