Question

JUST NEED CHECKED!!
Suppose that x* means 5x^2 - x then what does (y+3)* mean?

Do you plug in (y+3) for x, expand the squared, and the (y+3)'s cross out to 5(y+3)?
(y+3)* = 5y+15

Answer 1

Interesting...

Answer 2

x* = 5x^2 - x
y* = y+3

just a guess

Answer 3

My thought would be that x* is like a function. f(x) = 5x^2-x
x* = 5x^2-x
(y+3)* = 5(y+3)^2-(y+3)

Answer 4

I think so too. But wouldn't you expand it after that?
5(y+3)(y+3)-(y+3)
Then the (y+3)s cross out leaving just 5(y+3)?

Answer 5

Yeah, that probably is right. the y variable threw me off

Answer 6

Yes. I think you should go ahead and square and then collect like terms.

Answer 7

Okay, I think my final answer is 5y+15, since (y+3) are like terms.

Answer 8

\[5(y+3)^{2}-(y+3)=5(y^2+6y+9)-y-3=5y^2+30y+45-y-3\]

Answer 9

\[5y^2+29y+42\]

Answer 10

So the last (y+3) doesn't cross out anything?

Answer 11

Doesn't take a y out of the squared term?

Answer 12

Remember the "powers first" rule in order of operations.

Answer 13

This could be the approach you favor:

Answer 14

\[5(y+3)^2-(y+3)=(y+3)[5(y+3)-1]=(y+3)[5y+15-1]=\]

Answer 15

\[(y+3)(5y+14)=5y^2+14y+15y+42=5y^2+29y+42\]

Answer 16

Thank you so much! You really helped. :)

Answer 17

yw