Question

Fan and medal***

If (8z − 9)(8z + 9) = az^2 − b, what is the value of a?

The value of a is____

Answer 1

Probably as a first step you should multiply the two parentheses on the left. That may help you get started on the problem. Are you comfortable with doing that?

Answer 2

yes, let me multiply

Answer 3

Alright, sounds good. :)

Answer 4

64z^2- 81 I don't know if I did right

Answer 5

You did it perfectly! Nice job

Answer 6

Now look closely at the two equations they gave you
64z^2 - 81 = az^2 - b

notice that they both "look" the same. They both have a z^2 term. They both have a subtraction. And they both have "something" in front of the z^2 term.

Answer 7

yes,i see so what I need to do now?

Answer 8

Well, we can simply look and visually see that "a" must be 64. There is no other way that these two equations can be equal. In fact, for a bonus, I can also see that "b" must be 81.

Answer 9

Mathematicians call this "having the same form." We were able to take the parentheses and transform them into an equation that had the same form as the equation on the right. Then, solving the problem is easy and we can trust our intuition.

Answer 10

It's a little bit of a stretch to see it. So let me know if you have any questions. :)

Answer 11

so wait, its the answer its 81

Answer 12

Not quite. They want to know what the value of "a" is. "a" must be 64. I threw in the part about b as a bonus just so you could see that as well.

Answer 13

Basically, the question just wants you to answer "What is the number in front of the z^2?" Instead of keeping it simple, though, they tried to get fancy by setting equations equal. It's the same thing though.

Answer 14

yea I see can you check my answer for a different question please I already have the answer I just want to check

Answer 15

go ahead! :)

Answer 16

Choose the correct simplification of 7x^2(6x + 3x^2 − 4).
my answer: 21x^4 + 42x^3 - 28x^2

Answer 17

Yep looks good. They tried to trick you be playing the 3x^2 in the middle, but looks like you got it. And you kept all the signs straight. Nice!